Question

What value of θ makes cosθ = sin70° a true statement?

A) 20°
B) 40°
C) 70°
D) 90°

Answer 1

A

Explanation:

Answer 2

A) 20°

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.