Converting Between Sine and Cosine Using Cofunction Identities

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Two positive angles are complements if their sum is 90° or π/( 2 ). Any pair of trigonometric functions f and g for which f(θ)=g(90°− θ) and g(θ)=f(90°− θ) are called cofunctions.


The value of a trigonometric function of θ is equal to the cofunction of the complement of θ. Cofunctions of complementary angles are equal.

sin⁡〖θ=cos⁡(90°−θ) 〗 cos⁡〖θ=sin⁡(90°−θ) 〗
tan⁡θ=cot⁡(90°−θ) cot⁡θ=tan⁡(90°−θ)
sec⁡θ=csc⁡(90°−θ) 〖 csc〗⁡θ=sec⁡(90°−θ)

Q. Find a cofunction with the same value as the given expression:

a) sin⁡〖46°〗

b) cot⁡〖π/( 12 )〗