For what angle measure must sine and cosine have the same value? Explain how you know.

Sine and Cosine function have similar value for 45° or π/4 and the value is

1/√2

Step-by-step explanation:

Sine and Cosine function have similar value at an angle of 45

It must be remembered that sine and cosine are complementary functions.

Hence, Sin ∅ = Cos (90-∅)

Since for complimentary function both angles must some to 90 degrees

Hence ∅=90-∅

2∅=90

∴ ∅ = 45 degrees

The above answer can be verified from the graph of sine and cosine functions where sine and cosine functions intercept each other at 45 degrees. Since the sine and cosine functions are cyclical, hence for every π+45 degrees, the value would repeat itself.