please help.

Question

Given that sinA 5/8 and that <A is located in the second quadrant , determine exact value for the other two primary trigonometric ratios. including sketch pls

Answer 1

The trigonometric function value of sin(A) = 5/8.

To find the value of cos(A), using the Pythagorean identity : sin²(θ) + cos²(θ) = 1, we obtain

(5/8)² + cos²(A) = 1

cos²(A) = 1 - 25/64 = 39/64.

Because cos(A) < 0 in quadrant II, we can use the negative root to obtain

cos(A) = - √39/√64 = - √39/8.

Using the Quotient identity : tan(A) = sin(A)/cos(A), we obtain

tan(A) = (5/8) / (- √39/8) = - 5/√39.

Graph :