Given that sin 59 ≈ 0.857, enter the cosine of a complementary angle.

The cosine of a complementary angle is cos (90° - 59°) ≈ 0.857.

Solution:

Given that sin 59° ≈ 0.857.

To find the cosine of a complementary angle.

If two angles are complementary means, their sum is add up to 90°.

Complementary angle of 59° is (90° - 59° = 31°).

We know that,

The sine of any acute angle is equal to the cosine of the complementary angle.

That is sinθ = cos (90 - θ).

⇒ sin 59° = cos (90° - 59°)

≈ 0.857

Therefore the cosine of a complementary angle is cos (90° - 59°) ≈ 0.857.