Question

What value of θ makes cosθ = sin70° a true statement? A) 20° B) 40° C) 70° D) 90°

Answer 1

Answer:

A) 20°

Step-by-step explanation:

Sine and cosine are co-function complements which means that value of sine of an angle is equal to the value of cosine of the complementary angles.

This can be represented by:

$\sin\theta=\cos(90\°-\theta)$

$\cos\theta=\sin(90\°-\theta)$

Given statement:

$cos\theta=\sin70\°$

Applying co-function complements

$\cos\theta=\sin(90\°-\theta)$

Since, we can represent 70° = 90°-20°

So

$\cos20\°=\sin(90\°-20\°)$  

Thus, $\theta=20\°$ makes the statement true.