Trigonometry Table: Formula, Trigonometry Ratio Table

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Trigonometry table includes the values of trigonometric functions for standard angles such as 0°, 30°, 45°, 60° and 90° in a tabular form. Trigonometry is a branch of mathematics that deals with the measurement of angles, the relation between the angles and sides of triangles.

The use of trigonometry ratio tables is mainly seen in finding the length, angle and tangent of a right triangle whose one angle is always 90°.
The trigonometric table includes trigonometric ratios such as sine, cosine, cosecant, secant, tangent and cotangent.
While solving trigonometric problems in mathematics, these ratios can be written as cos, sine, cosec, sec, tan and cot.
Different patterns can be found within trigonometry ratio table and between their corresponding angles.
Many geometric calculations become easy to figure out using trigonometry tables, trigonometry ratios and charts.

Furthermore, the use of trigonometric tables is seen in various fields such as engineering, science and navigation. In this article we will discuss about tricks, formulas and methods to be used while studying trigonometry table.

Table of Content

Introduction to Trigonometry Table
How to Make Trigonometry Table?
Trigonometry Table Formulas
Trigonometry Table Tricks
Things to Remember
Sample Questions

Introduction to Trigonometry Table

[Click Here for Sample Questions]

The trigonometry table focuses on relationships between side lengths and angles of a triangle. Also, the trigonometry chart comprises trigonometric ratios that are correlated with each other.

Trigonometric standard angles such as 0°, 30°, 45°, 60°, and 90° can be calculated using the trigonometry ratio table.
It consists of trigonometric ratios like sine, cosine, tangent, cosecant, secant, and cotangent.
It is easier to predict the values of the trigonometry table as there are certain patterns between the trigonometric ratios and angles.

Before creating the table, below are some important formulas that can be used while solving problems:

Trigonometry Ratio Formulas

Some trigonometric formulas to memorize the trigonometric table on the basis of the relationship between different trigonometric ratios are.

sin x = cos (90° – x)
cos x = sin (90° – x)
tan x = cot (90° – x)
cot x = tan (90° – x)
sec x = cosec (90° – x)
cosec x = sec (90° – x)
1/sin x = cosec x
1/cos x = sec x
1/tan x = cot x

An easy acronym to remember in the trigonometry ratio table is "SOHCAHTOA"!

SOH → Sine = Opposite/Hypotenuse
CAH → Cosine = Adjacent/Hypotenuse
TOA → Tangent = Opposite/Adjacent

Trigonometry Table for Standard Angles
Angles (In Degrees)	0°	30°	45°	60°	90°	180°	270°	360°
Angles (In Radians)	0°	π/6	π/4	π/3	π/2	π	3π/2	2π
SinΘ	0	1/2	\(\frac{1}{\sqrt{2}} \)	\({\sqrt{3}\over2} \)	1	0	-1	0
CosΘ	1	\({\sqrt{3}\over2} \)	\(\frac{1}{\sqrt{2}} \)	1/2	0	-1	0	1
TanΘ	0	\(\frac{1}{\sqrt{3}} \)	1	\(\sqrt{3}\)	∞	0	∞	0
CosecΘ	∞	2	\(\sqrt{2}\)	\(\frac{2}{\sqrt{3}} \)	1	∞	-1	∞
SecΘ	1	\(\frac{2}{\sqrt{3}} \)	\(\sqrt{2}\)	2	∞	-1	∞	1
CotΘ	∞	\(\sqrt{3}\)	1	\(\frac{1}{\sqrt{3}} \)	0	∞	0	∞

Important Pointers Related to Trigonometry Table

The values for complementary angles like 30° and 60° can be calculated using complementary formulas for trigonometric ratios.
The value for some ratios in a trigonometry table is ∞ or "not defined". This is because any number when divided by "0" gives an undefined value which is equivalent to infinity.
In mathematics, six important and commonly used trigonometric functions are "sine function", "cosine function", tan function, "cot function", "sec function" and "cosec function".
There is a change of sign in the values under 180° and 270° in a trigonometric table due to the change in the quadrant.

How to Create a Trigonometry Table?

[Click Here for Sample Questions]

The steps to create a Trigonometry Table are as mentioned below:

Step 1 - Creating a Table

Create the trigonometry table with the required angles (0°, 30°, 45°, 60°, and 90°) in the top row and all six trigonometric functions sine, cosine, tangent, cosecant, secant, and cotangent in the first column.

Also Check: Difference between Trigonometry and Geometry

Step 2 – Determine Values of Sine of the Required Angle

To find the value of sin, divide all the values 0, 1, 2, 3, and 4 by 4 and then take the square root, respectively.

For example

Value of 0°= (0/4) = 0
Value of 30°= (1/4) = 1/2.

As a result, the corresponding values from 0 to 360° are as follows:

Angles	0°	30°	45°	60°	90°	180°	270°	360°
Sin	0	1/2	1/√2	√3/2	1	0	-1	0

Step 3 – Values of Cosine of the Required Angle in the Trigonometry Table

The values of cos are opposite to those of sin angles.

This means that the value of sin (0 - x) degree is equal to the value of cos (90°- x).
To calculate the value of cos in the Trigonometry table, divide the opposite order of sin, i.e., 4, 3, 2, 1, and 0 by 4 and take the square root.

For example

Value of 0° = (4/4) = 1
Value of 30° = (3/4) = 3/ 2

As a result, the corresponding values from 0 to 360° are as follows:

Angles	0°	30°	45°	60°	90°	180°	270°	360°
cos	1	√3/2	1/√2	1/2	0	-1	0	1

Step 4 – Determine Values of Tangent of the Required Angle

Sine divided by cosine equals the tangent. Thus, tan x = sin x/cos x
To find the value of tan 30, divide sin 30 by cos 30 and get the required value, i.e., (1/2)/\({\sqrt{3}\over2} \) = \(\frac{1}{\sqrt{3}} \)

The other corresponding values are:

Angles	0°	30°	45°	60°	90°	180°	270°	360°
tan	0	1/√3	1	√3	∞	0	∞	0

Step 5 – Determine Values of Cot for Required Angles in Trigonometry Table

The value of Cot is the inverse of the value of Tan.

As a result, the value of the cot in the Trigonometry table for each value is 1/tan.
Since tan x = sin x/cos x
Hence, cot x = cosx/sin x

As a result, the corresponding values are simply the reciprocal of the tan values.

Angles	0°	30°	45°	60°	90°	180°	270°	360°
cot	∞	√3	1	1/√3	0	∞	0	∞

Step 6 – Values of Cosecant

The value of cosec of any angle is equal to the inverse of sin on that angle. As a result, the corresponding values will be the reciprocal of the sin x values in the Trigonometry table.

Angles	0°	30°	45°	60°	90°	180°	270°	360°
cosec	∞	2	√2	2/√3	1	∞	-1	∞

Step 7 – Values of Secant in Trigonometry Table

Any angle's value of sec is equal to the inverse of the value of cos of that angle in the Trigonometry table.

Angles	0°	30°	45°	60°	90°	180°	270°	360°
sec	1	2/√3	√2	2	∞	-1	∞	1

Also Read: Derivative of Inverse Trigonometric Functions

Trigonometry Table Formulas

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Important Trigonometry Table Formulas are provided below:

Compound Angles

cos A cos B – sin A cos B = cos (A + B)
cos A cos B + sin A cos B = cos (A – B)
sin A cos B + cos A sin B = sin (A + B)
sin A cos B – cos A sin B = sin (A – B)
sin2 A – sin2 B = sin (A + B) sin (A – B) = cos² B – cos² A
cos² A – sin² A – sin² B = cos (A + B) cos (A – B) = cos² B – sin²A
(tan A + tan B)/(1 – tan A tan B) = tan (A + B)
(tan A – tan B)/(1 + tan A tan B) = tan (A – B)
sin2A = sin (A + A) = sinA.cosA + cosA.sinA = 2sinA.cosA

Example: Prove that sin(45° + θ) − sin(45° − θ) = √2 sinθ.

Solution: L.H.S = sin(45° + θ) − sin(45° − θ)
= sin 45°cos θ + cos 45°sinθ-(sin 45°cosθ - cos 45°sin θ)
= sin 45°cos θ + cos 45°sinθ - sin 45°cosθ + cos 45°sin θ
= 2cos 45°sin θ = 2(1/√2) sin θ = √2 sin θ ⇒ R.H.S
∴ Hence, proved.

Example: Taking a = 60° and B = 30°, verify with Trigonometry table that, sin (A -B) = sin A cos B – cos A sin B.

Solution: A = 60° and B = 30° ⇒ A – B = 30°

∴ sin (A – B) = sin 30° = 1/2

sin A cos B – cos A sin B = sin 60° cos 30° – cos 60° sin 30° = (√3/2 x √3/2 – 1/2 x 1/2) = (3/4 – 1/4) = 2/4 = 1/2

∴ sin (A – B) = sin A cosB – cos A sin B.

Read About: Trigonometric Identities

Sum and Differences of Sines and Cosines

sin (A+B) + sin (A-B) = 2 sin A cos B
sin (A+B) – sin (A-B) = 2 cos A sin B
cos (A+B) + cos (A-B) = 2 cos A cos B
cos (A-B) – cos (A+B) = 2 sin A sin B

Example: Using the formula for the cosine of the difference between two angles, find the exact value of \(cos (\frac{5 \pi}{4} - \frac{\pi}{6})\).

Solution: Begin by writing the formula for the cosine of the difference between two angles. Then substitute the given values through Trigonometry table:

⇒ \(cos (\alpha-\beta)=cos \alpha cos\beta + sin \alpha sin\beta\)

⇒ \(cos (\frac{5\pi}{4}-\frac{\pi}{6})= cos (\frac{5\pi}{4}) cos (\frac{\pi}{6})+sin(\frac{5\pi}{4})sin(\frac{\pi}{6})\)

\(=(\frac{-\sqrt {2}}{2}) (\frac{\sqrt {3}}{2}) - (\frac{\sqrt {2}}{2})(\frac{1}{2})\)

\(=\frac{\sqrt{-6}}{4} - \frac{\sqrt{2}}{4} \)

\(=\frac{-\sqrt{6}{-\sqrt{2}}}{4}\)

Read More: 30 60 90 formula

Trigonometric Ratios of Multiples of Angles

sin(2A) = 2sin(A) cos(A) = [2tan A/(1+tan²A)]
cos(2A) = cos²(A)–sin²(A) = [(1-tan² A)/(1+tan² A)]
cos(2A) = 2cos2(A)−1 = 1–2sin2(A)
tan(2A) = [2tan(A)]/ [1−tan²(A)]
sec (2A) = sec² A/(2-sec²A)
cosec (2x) = (sec A. cosec A)/2
Sin 3A = 3 sin A – 4sin3A
Cos 3A = 4cos3A-3cos A
Tan 3A = [3tanA-tan³A]/[1-3tan²A]

Example: What is the value of sec θ when θ is 45°?

Solution: The value of cos 45° is 1/√2 and secant is inverse to cos.

Thus, \(sec \theta = \frac{1}{cos \theta} = \frac{1}{\frac{1}{\sqrt{2}}}\)

Example: Find the value of sec² 42° – cosec² 48°.

Solution: The solution of the above equation is as follows:

sec² 42° – cosec² 48° = sec² 42° – cosec² (90° – 42°)

= sec² 42° – sec² 42° [using secθ = cosec(90° – θ)]

Multiples and Submultiple Angles

2 sin A cos A = 2 tan A/(1 + tan²A) = sin 2A
cos 2A – sin2A = 2cos2A - 1 = 1 - 2 sin2A = cos 2A
4 cos 3A – 3 cos A = cos 3A
3 sin A – 4 sin 3A = sin 3A
2 tan A/(1 - tan²A) = tan 2A
(3 tan A- tan³A)/(1 - tan2A) = tan 3A

Example: Without using a Trigonometry table, prove that sin 12° sin 48° sin 54˚ = 1/8

Solution: L. H. S. = sin 12° sin 48° sin 54°

= 1/2 (2 sin 12°sin 48°) sin (90°- 36°)

= 1/2 [cos 36°- cos 60°] cos 36°

\(= \frac{1}{2}[\sqrt \frac{\sqrt{5+1}}{4}-\frac {1}{2}]\)

\(=\frac{\sqrt{5}+1}{4}\)

Also Read: Quadrant

Inverse Trigonometry Formula

sin^-1 (–A) = – sin^-1 A
cos^-1 (–A) = π – cos^-1 A
tan^-1 (–A) = – tan^-1 A
cosec^-1 (–A) = – cosec^-1 A
sec^-1 (–A) = π – sec^-1 A
cot^-1 (–A) = π – cot^-1 A

Example: Find the values of sin (cos⁻¹−1 3/5).

Solution: Let, cos⁻¹−1 3/5 = θ
Therefore, cos θ = 3/5
Therefore, sin θ = √(1 - cos2²θ) = √(1 - 9/25) = √(16/25) = 4/5 .
Therefore, sin (cos⁻¹−1 3/5) = sin θ = 4/5.

Example: Find the value of x, for sin(x) = 2.

Solution: As given in the question,

sin x = 2

x = sin^-1(2), is not possible.

\(\therefore\) There is no value of x for which sin x = 2; since the domain of sin^-1x is -1 to 1 for the values of x.

Also check: Graphs of Inverse Trigonometric Functions

Trigonometry Table Tricks

[Click Here for Sample Questions]

Memorizing the trigonometry table can be a hectic task but its importance during the calculation is well known. It becomes relatively easier with the understanding of trigonometry formulas. Here are some key points and tricks to understand and memorize the trigonometry table:

Trigonometry Table Tricks

The most common trigonometry table tricks to learn the complex trignometric table can be given as:

sin (reciprocal of cosecant) = opposite/ hypotenuse
cos (reciprocal of secant) = adjacent/hypotenuse
tan (reciprocal of cotangent) = opposite/adjacent
cot (reciprocal of tangent) = adjacent/opposite
cosec (reciprocal of sine) = hypotenuse/opposite
sec (reciprocal of cosine) = hypotenuse/adjacent

Things to Remember

Trigonometric Values are based on 3 trigonometric ratios – Sin, Cos, and Tan.
In Trigonometry table, we get Sine θ = Side opposite to θ/Hypotenuse
Cosines θ = Adjacent side to θ/Hypotenuse
Tangent θ = Side opposite to θ/Adjacent side to θ
The standard angles in a trigonometric table are 0°, 30°, 45°, 60°, and 90°.
All the values of higher angle functions in the trigonometric table can be easily calculated from the standard angle values.
The value of Cot is the inverse of the value of Tan. As a result, the cot x = 1/tanx.
The value of cosec of any angle is equal to the inverse of sin on that angle. This implies that- cosec x = 1/ sec x.
Any angle's value of sec is equal to the inverse of the value of cos of that angle, i.e. sec x = 1/ cos x.

Sample Questions

Ques: What are the uses of Trigonometry Table in real life? (1 Mark)

Ans: A trigonometry ratio table is used to find the distance between objects in space as well as land. Trigonometry table helps to enhance the precision of calculation.

Ques: How to memorize trigonometry table? (1 Mark)

Ans: To keep the trigonometry ratio table in mind, use the acronym "SOHCAHTOA". The full form of "SOHCAHTOA" is Sine opposite hypotenuse, adjacent cosine hypotenuse, tangent opposite adjacent. For example, in case you wanted to calculate the sine of an angle or triangle, you should have to know that sine is "sine opposite hypotenuse" primarily based totally on "SOHCAHTOA".

Ques: Evaluate: 1 – Tan²45 / 1 + Tan²45. (2 Marks)

Ans: The value of Tan 45°

Tan 45° = 1

Therefore,

1 – Tan²45 / 1 + Tan²45 = 1-1/1+1

= 0/2

= 0

Ques: Evaluate Sin 60° Cos 30° + Sin 30° Cos 60°. (2 Marks)

Ans: We know that:

Sin 60°= √3/ 2

Cos 30°= √3/2

Sin 30°= 1/2

Cos 60°= 1/2

So,

Sin 60°Cos 30° + Sin 30°Cos 60° = √3/ 2 . √3/2 + 1/2.1/2

4/4 = 1

Ques: If Sec 4A=Cosec(A – 20°), where 2A is an acute angle, find the value of A. (2 Marks)

Ans: Sec 4A=Cosec ( A-20° )

Cosec ( 90 - 4A) = Cosec (A- 20° )

90 – 4A = A – 20

110 = 5A

A = 22°

Ques: Express Sin 67° + Cos 75° in terms of trigonometric ratios of angles between 0° and 45°. (2 Marks)

Ans: Sin 67° + Cos 75°

= Sin (90 – 23)°+Cos (90 – 27)°

= Cos 23° +Sin 25°

So, Sin 67° + Cos 75° can also be expressed as Cos 23° + Sin 25°

Ques: Evaluate: Sin 25° Cos 65° + Cos 25° Sin 65°. (2 Marks)

Ans: Sin (90 – 65)° Cos 65° + Cos (90 – 65)° Sin 65°

= Cos 65°Cos 65° + Sin 65° Sin 65°

Cos2 65°+Sin 2 65° = 1

Ques: If sec 4A = cosec ( A – 20°) where 4A is an acute angle, Find the value of A. (2 Marks)

Ans: Given that:

Sec 4A = cosec (A-20°)

Cosec (90°-4A) = cosec(A-20°)

90° - 4A = A-20°

110°= 5A

A=22°

Ques: Evaluate 4(sin⁴30° + cos⁴60°)- 3(cos²45° – sin²90°). (2 Marks)

Ans: Given that-

=4(sin⁴30° + cos⁴60°)- 3(cos²45° – sin²90°)

=4[(1/2)⁴ + [(1/2)⁴] – 3[(1/2)² -1 ]

=4[1/16 + 1/16] – 3[1/2 - 1]

= 4*2/16-3(-1/2)

= 1/2 + 3/2 = 4/2 =2

Ques: If tan2A = cot (A-18°), where 2A is an acute angle, Find the value of A. (3 Marks)

Ans: Given that:

tan2A = cot (A-18°)

tan2A – cot (90° – 2A)

Substituting the values,

Cot(90° – 2A ) = cot (A-18° )

Therefore,

90° – 2A = A-18°

108° = 3A

A= 108°/3

Hence, The value of A = 36°

Ques: If tan2A = cot (A - 18°), where 2A is acute angle, find the value of A. (2 Marks)

Ans: Given that:

tan2A = cot (A - 18°)

tan2A = tan (90- A-18°)

tan2A = tan 108°-A

2A = 108° – A

3A = 108°

A = 36°

Ques: Consider right triangle ABC, right-angled at B. If AC = 17 units and BC = 8 units determine all the trigonometric ratios of angle C. (5 Marks)

Ans: Given Data

Length of the side BC = 8 units

Length of the side AC = 17 units

q1-triangle2

Step 1: Calculate the length of AB

In \(\Delta\)ABC, using Pythagoras theorem, AB = \(\sqrt{AC^2-BC^2}=\sqrt{17^2-8^2}\)

\(\sqrt{289-64}=\sqrt{225}\)

\(\Rightarrow\) AB = 15 units

Step 2: Calculate the trigonometric ratios of angle C

sin C = \(\frac{opposite side}{hypotenuse} = \frac{AB}{AC} = \frac{15}{17} \)

cos C = \(\frac{adjacent side}{hypotenuse} = \frac{BC}{AC} = \frac{8}{17} \)

tan C = \(\frac{opposite side}{adjacent side} = \frac{AB}{BC} = \frac{15}{18} \)

cot C = \(\frac{1}{tan C}=\frac{adjacent side}{opposite side} = \frac{BC}{AB} = \frac{8}{15} \)

sec C = \(\frac{1}{cos C}=\frac{hypotenuse}{adjacent side} = \frac{AC}{BC} = \frac{17}{8} \)

cosec C = \(\frac{1}{sin C}=\frac{hypotenuse}{opposite side} = \frac{AC}{AB} = \frac{17}{15} \)

Ques: In triangle PQR, right angled at Q if PR = 41 units and PQ – QR = 31. Find sec²R – tan²R. (5 Marks)

Ans: PQR with right angled at Q

PR = 41 units

PQ - QR = 31

PQ - QR = 31 → PQ = 31 + QR

q11 triangle

Step 1: Compute QR and PQ

Using Pythagoras Theorem, PR² = PQ² + QR²

41² = (31 + QR)² + QR²

1681 = 961 + 62QR + QR² + QR²

2QR² + 62QR – 720 = 0

Divide the equation by 2: QR² + 31QR – 360 = 0

Factorize QR² + 31QR – 360 = 0 QR² + 40 QR – 9QR – 360 = 0

QR(QR + 40) – 9(QR + 40) = 0

(QR + 40) (QR – 9) = 0

QR = -40 or QR = 9

QR cannot be negative ∴ QR = 9

PQ = QR + 31 = 9 + 21 = 40

Step 2: Calculate sec²R – tan²R

sec R = \(\frac{hypotenuse}{side adjacent to ?R} = \frac{PR}{QR} = \frac{41}{9}\)

tan R = \(\frac{side opposite to ?R}{side adjacent to ?R} = \frac{40}{9}\)

sec²R – tan²R = \(\frac{41^2}{9^2}-\frac{40^2}{9^2}\)

\(\frac{(41+40)\times(41-40)}{81} = \frac{81}{81} = 1\)

Thus, sec²R – tan²R = 1

Ques. If cos A = 4/5, then tan A = ? (2 marks)

Ans: Given that, cos A = 4/5

and we know that, cos θ = base/hypotenuse

here, base = 4 and hypotenuse = 5

then, using Pythagorus Theorem

Height = \(\sqrt{5^2-4^2}=\sqrt{9}\)

Height = 3

Now, tan θ = height/base

Therefore,

tan A = 3/4

Ques. If tan θ = 3/4, then cosec θ =? (2 marks)

Ans. Given that, tan θ = 3/4 = height/base

using Pythagorus Theorem

Hypotenuse = \(\sqrt{3^2+4^2}=\sqrt{25}\)

Hypotenuse = 5

Therefore,

cosec θ = hypotenuse/height = 5/3

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Trigonometry Table: Formula, Trigonometry Ratio Table

Introduction to Trigonometry Table

Trigonometry Ratio Formulas

Important Pointers Related to Trigonometry Table

How to Create a Trigonometry Table?

Step 1 - Creating a Table

Step 2 – Determine Values of Sine of the Required Angle

For example

Step 3 – Values of Cosine of the Required Angle in the Trigonometry Table

For example

Step 4 – Determine Values of Tangent of the Required Angle

Step 5 – Determine Values of Cot for Required Angles in Trigonometry Table

Step 6 – Values of Cosecant

Step 7 – Values of Secant in Trigonometry Table

Trigonometry Table Formulas

Compound Angles

Sum and Differences of Sines and Cosines

Trigonometric Ratios of Multiples of Angles

Multiples and Submultiple Angles

Inverse Trigonometry Formula

Trigonometry Table Tricks

Trigonometry Table Tricks

Things to Remember

Sample Questions

CBSE X Related Questions

1.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

2.
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

3.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

4.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

5.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

6.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

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Trigonometry Table: Formula, Trigonometry Ratio Table

Introduction to Trigonometry Table

Trigonometry Ratio Formulas

Important Pointers Related to Trigonometry Table

How to Create a Trigonometry Table?

Step 1 - Creating a Table

Step 2 – Determine Values of Sine of the Required Angle

For example

Step 3 – Values of Cosine of the Required Angle in the Trigonometry Table

For example

Step 4 – Determine Values of Tangent of the Required Angle

Step 5 – Determine Values of Cot for Required Angles in Trigonometry Table

Step 6 – Values of Cosecant

Step 7 – Values of Secant in Trigonometry Table

Trigonometry Table Formulas

Compound Angles

Sum and Differences of Sines and Cosines

Trigonometric Ratios of Multiples of Angles

Multiples and Submultiple Angles

Inverse Trigonometry Formula

Trigonometry Table Tricks

Trigonometry Table Tricks

Things to Remember

Sample Questions

CBSE X Related Questions

1.Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent. Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

2.The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

3.In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

4.A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

5.In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

6.An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

2.
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

3.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

4.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

5.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

6.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is