Cos Square Theta Formula: Trigonometric Ratio & Types

Cos Square Theta Formula is, Cos ² theta= 1 – sin² theta. The function of an angle, that is the angles and sides relationships are given by trigonometric functions. The equations which relate to the variety of trigonometric functions for any variable are referred to as trigonometric identities. 

As per the trigonometric identities, the cos square theta formula is represented by:

The sine or sin, the cosine or cos, the tangent or tan, the cotangent or cot, the cosecant or cosec, and the secant or the sec are the six trigonometric signs. Trigonometry is a branch of mathematics in geometry that was discovered to deal with the ideas and problems of right-angled triangles. And hence, these trigonometric signs are used for the calculation of sides and angles in general.

Also read: Isosceles Triangle Theorems

Key Terms: Sin, Sin Squared X, Triangle, Pythagoras Theorem, Cosine, Secant, Cosecant, Tangent, Cotangent, Perpendicular, Hypotenuse, Integrals, Trigonometric Ratio, Trigonometry

---

What are Trigonometric Ratios?

[Click Here for Sample Questions]

Trigonometric ratios are the value of the trigonometric functions that are on the basis of the value of the ratio of sides of a right-angled triangle or an orthogonal triangle. The three sides of a right-angled triangle are as follows:

• The hypotenuse (longest edge)
• The perpendicular (the opposite side of the hypotenuse)
• The base (the adjacent side to the angle to be considered)

The trigonometric ratios are defined as,

Trigonometric Functions Detailed Video Explanation

Types of Trigonometric Ratios

There are six different trigonometric ratios, which are as follows:

• Sine or the sin
• Cosine or the cos
• Tangent or the tan
• Cosecant or the cosec
• Secant or the sec
• Cotangent or the cot.

Let there be a right-angled triangle given in the figure whose rations are taken for an angle C:

The formulas will be:

• Sine = perpendicular/hypotenuse = AB/AC
• Cosine = Base/hypotenuse = BC/AC
• Tangent = perpendicular/base = AB/BC
• Cosecant = 1/sin = hypotenuse/perpendicular = AC/AB
• Secant = 1/cos = hypotenuse/base = AC/BC
• Cotangent = 1/tan = base/perpendicular = BC/AB

Also read: Determinant Formula

---

Cos Square Theta

[Click Here for Previous Year Questions]

Cos square theta is a double-angle formula that is used in trigonometry for solving different complex problems. It has got its use in calculus as well. Other than the primary trigonometric signs such as sin, cos, and tan, these double-angle formulas are also important in trigonometry.

Examples Based on Cos Square Theta

Example: Determine the value of cosθ, with the value of sinθ given as 3/5.

Ans: The value of sinθ is given as = 3/5

Now, by using the cos square formula, we can obtain:

⇒ cos²θ + sin²θ = 1

⇒ cos²θ = 1 – sin²θ = 1 – (3/5)² = 1 – 9/25

⇒ cos²θ = 16/25

⇒ cosθ = √(16/25) = ± 4/5

Thus, the value of cosθ is ± 4/5.

Example: Determine the value of cos2θ, with the value of cosθ given as = 1/2.

Ans: By applying a generalized formula,

⇒ cos2θ = 2cos²θ – 1

The value of cos2θ, after substituting the value is, cosθ = 1/2

Hence,

⇒ cos2θ = 2 × (1/2)² – 1 = 2/4 – 1 = 1/2 – 1 = – 1/2

Accordingly, cos2θ = – 1/2.

Also Read:

---

Cos Square Theta Formula

[Click Here for Sample Questions]

The basic formula to obtain the value of cos square theta is,

cos² x + sin² x = 1

Where, the basic formula for

sin = perpendicular/hypotenuse and

cos = base/hypotenuse.

By shifting the sin square x in the above formula to the right-hand side we get the formula for cos square x.

So, the formula will be,

Cos² x = 1 - sin² x

Also, some other formulas derived from the above expression for cos square theta are:

• Cos 2x = cos² x - sin² x
• Cos 2x = 2cos² x – 1

---

Things to Remember

• Trigonometric ratios are the value of the trigonometric functions that are based on the ratio of the primary trigonometric signs.
• The right-angled triangle has three edges, the hypotenuse, the perpendicular, and the base.
• The six trigonometric ratios are sine, cosine, tangent, cotangent, cosecant, and secant.
• The ratios are expressed as: Sin x = perpendicular/hypotenuse; Cos x = base/hypotenuse; Tan x = perpendicular/base; Cosec x = 1 / sin; Sec x = 1 / cos; Cot X = 1 / tan.
• The formula for cos square theta is, Cos²x = 1 – sin².
• Other formulas of cos square theta are: Cos square x = cos 2x + 1; Cos square x = cos 2x + sin square x.

Also read:

---

Previous Year Questions

• ABCD is a trapezium such that AB and CD are parallel… (JEE Main 2013)
• The general solution of sin 3x + sinx… (AMUEEE 2013)
• Consider a triangular plot ABC with sides AB = 7m… (JEE Main 2019)
• If the angles A,B, and C of a triangle are in an… (JEE Advanced 2010)
• The number of solutions of 2 sinx + cosx = 3 is… (WBJEE 2011)
• If a is a positive integer, then the number of values... 
• The integral ∫cos (logx) dx is equal to… (JEE Main 2019)
• The number of integral terms in the expansion…
• \(\int\limits_{0} ^{1}\frac{dx}{[ax+b(1 x)]^2} \) is equal to…
• Prove that the value of the integral... (JEE Advanced 1988)