Cos Square Theta Formula

Trigonometric identities are equations that are true for any value of the variable in the domain and relate to various trigonometric functions. An identity is a mathematical equation that holds true for all values of the variables in it. Trigonometric functions define the function of an angle, i.e. the angles and sides relationships. The trigonometric functions are sin, cosine, tangent, cotangent, Cos, Cosec.

Formula for Cos Square theta

According to the trigonometric identities, we know that,

cos²θ + sin²θ = 1

where,

θ is an acute angle of a right triangle.
sinθ and cosθ are the trigonometric ratiosgiven as follows:
sinθ = Altitude/Hypotenuse
cosθ = Base/Hypotenuse
sin2θ is the square of sinθandcos2θ is the square ofcosθ i.e,
sin²θ = (sinθ)²
cos²θ= (cosθ)²

Thus cos square theta formula is given by,

cos²θ = 1 -sin²θ

Solved Example for Cos Square Theta Formula

Example: What is the value of cos square x, if Sin x = 4/5 ?

Sol: Using Cos Square theta formula,

Cos²x = 1 Sin²x

= 1 (4/5)²

= 1 16/25

= (25 16) / 25

= 9/25

Thus, cos x = 3/5

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Cos Square Theta Formula