Question

If sin ß= 0.27 and ß is an acute angle, what are
the cosine and tangent of ß?

Answer 1

To find the cosine and tangent of β, we can use the trigonometric identity:

sin² β + cos² β = 1

Given that sin β = 0.27, we can substitute this value into the identity:

(0.27)² + cos² β = 1

Simplifying the equation:

0.0729 + cos² β = 1

cos² β = 1 - 0.0729

cos² β = 0.9271

Taking the square root of both sides:

cos β ≈ ± √0.9271

Since β is an acute angle, the cosine function is positive in the first quadrant. Therefore, we take the positive value:

cos β ≈ √0.9271

cos β ≈ 0.9621

To find the tangent of β, we can use the trigonometric identity:

tan β = sin β / cos β

Substituting the given values:

tan β = 0.27 / 0.9621

Calculating the value:

tan β ≈ 0.2809

Therefore, the cosine of β is approximately 0.9621 and the tangent of β is approximately 0.2809.