Sin Cos Tan: Formula, Table & Values

Sin, Cos and Tan are the basic trigonometric ratios used to examine the relationship between the angles and sides of a triangle (especially of a right-angled triangle). Sin, Cos and Tan are the abbreviated forms of Sine, Cosine and Tangent respectively. These can be represented in terms of the sides (opposite side, adjacent side and hypotenuse) respective to the angle of a right-angled triangle. The formula for sin, cos and tan can be represented as follows.

• Sin θ = \(\frac {Opposite} {Hypotenuse}\)
• Cos θ = \(\frac {Adjacent} {Hypotenuse}\)
• Tan θ = \(\frac {Opposite} {Adjacent}\)

In trigonometry, sin cos and tan values are the essential functions that are considered while solving trigonometric problems. These trigonometry values help measure the angles and sides of a right-angle triangle. Along with sine, cosine and tangent values, the other three values included are cotangent, secant and cosecant. When the sin cos and tan values for a triangle are determined, the angles 0°, 30°, 45°, 60° and 90° are considered.

Key Terms: Sin, Cos, Tan, Hypotenuse, Angle, Trigonometric Ratios, Value Table, Adjacent side, Opposite Side, Right Angle Triangle

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Sin, Cos and Tan Formula

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The formula of sin cos and tan can be understood with the help of a right-angle triangle:

In the above triangle, the longest side of the triangle that is opposite to the right angle is called the Hypotenuse. The side adjacent to θ is called the Adjacent (Base) and the side opposite to θ is called the opposite (Perpendicular).

One can find the value of any of the missing sides of the right-angle triangle by applying the following formula given in the table below:

From the above formulas:

Tan θ = sin θ/cos θ

Now, the formulas for other trigonometry ratios are:

• Cot θ = 1/tan θ = Adjacent side/ Side opposite
• Sec θ = 1/Cos θ = Hypotenuse / Adjacent side
• Cosec θ = 1/Sin θ = Hypotenuse / Side opposite

Also,

• Tan θ = sin θ/cos θ
• Cot θ = cos θ/sin θ
• Sin θ = tan θ/sec θ
• Cos θ = sin θ/tan θ
• Sec θ = tan θ/sin θ
• Cosec θ = sec θ/tan θ

Trigonometric Functions Detailed Video Explanation

Also Read:

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Sin, Cos, Tan Chart

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The values of the trigonometric functions are tabulated below.

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Use of Sin Cos Tan 

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In our daily lives, the trigonometry ratios sin, cos, and tan are used to calculate heights and distances. Many real-life problems are solved using sin, cos, and tan. It is even used to calculate planetary motions and distances.

• It is used to calculate the angle of elevation, slope and heights of buildings, mountains, etc.
• It is used in the structural field to calculate the loads, roof slopes, flooring, etc.
• Trigonometry is used in flight engineering to calculate the angle change due to wind loads in flight aviation.
• It is even used by Archaeologists to calculate the excavations work.
• It is used in satellite systems.
• Trigonometry is used in marine engineering to design marine ramps.

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Finding Sin Cos Tan Values

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Here, to find the sin, cos, tan values, 

• Divide 0,1,2,3, and 4 by 4, then consider their positive roots of them.
• It can help get the sine ratios, which are, 0, ½, 1/√2, √3/2, and 1 for the angles 0°, 30°, 45°, 60° and 90°.
• Provide the values of sine degrees in reverse order in order to acquire values of cosine for the same angles.
• Since tan is the ratio of sin and cos, that is, tan θ = sin θ/cos θ, it can help acquire the values of the tan ratio for the specific angles.

Sin Values

For Sine Values,

• sin 0° = √(0/4) = 0
• sin 30° = √(1/4) = ½
• sin 45° = √(2/4) = 1/√2
• sin 60° = √3/4 = √3/2
• sin 90° = √(4/4) = 1

Cos Values

For Cos Values,

• cos 0° = √(4/4) = 1
• cos 30° = √(3/4) = √3/2
• cos 45° = √(2/4) = 1/√2
• cos 60° = √(1/4) = 1/2
• cos 90° = √(0/4) = 0

Tan Values

For Tan Values,

• tan 0° = 0/1 = 0
• tan 30° = (1/2) / (√3/2) = 1/√3
• tan 45° = (1/√2) / (1/√2) = 1
• tan 60° = [(√3/2)/(½)] = √3
• tan 90° = 1/0 = ∞

Hence, the sin cos tan values are found.

Also Read:

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Things to Remember 

• Sin, Cos and Tan are the basic trigonometric ratios used to examine the relationship between the angles and sides of a triangle.
• Sin θ is given by the ratio of the opposite side to the hypotenuse. It is given by Sin θ= Opposite/Hypotenuse = tan θ/sec θ
• Cos is given by the ratio of the adjacent side to the hypotenuse. It is given by Cos θ = Adjacent/Hypotenuse = sin θ/tan θ
• Tan θ is given by the ratio of sin θ to cos θ. It is given by Tan θ = Sin θ/Cos θ = Opposite / Adjacent.

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Previous Year Questions

1. If [x] denotes the greatest integer \le x≤x, then the system of linear equations….​[JEE MAIN 2019]
2. If ∠BPC=β, then tanβ is equal to :...​[JEE MAIN 2017]
3. Let P={θ:sinθ−cosθ=2​cosθ} and Q={θ:sinθ+cosθ=2​sinθ}….[JEE MAIN 2016]
4. If sinθ=1+t22t​ and ? lies in the second quadrant, then cosθ ….​[WBJEE 2011]
5. The number of solutions of 2sinx+cosx=3 is….…....​[WBJEE 2011]
6. Let tanα = a+1a​ and tanβ=2a+11​ then α+β is..[WBJEE 2011]
7. Let f(?)=(1+sin2?)(2−sin2?). Then for all values of ?….[WBJEE 2013]
8. Let p,q and rr be the sides opposite to the angles P,Q and R, respectively…..[WBJEE 2012]
9. If 0≤x<2π​ , then the number of values of x for which sinx−sin2x+sin3x=0, is...[JEE ADVANCED 2019]
10. The expression1−cotAtanA​+1−tanAcotA​ can be written as...[JEE ADVANCED 2013]
11. If ∠ADB=θ,BC=p and CD = qCD=q, then AB is equal to...[JEE ADVANCED 2013]
12. If the angles of elevation of the top of a tower from three collinear points….[JEE MAIN 2015]
13. The height (in mm) of the lamp-post is:….[JEE MAIN 2019]
14. If L=sin2(16π​)−sin2(8π​) and ,M=cos2(16π​)−sin2(8π​), then :….[JEE MAIN 2020]
15. If sum of all the solutions of the equation...[JEE MAIN 2018]

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