math20

Question

Given that sin A = 5/12 and That A is located on the second quadrant determine exact values for the other two primary trigonometric ratios. Including sketch

Answer 1

The trigonometric function value of sin(A) = 5/12.

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

(5/12)² + cos²(A) = 1

cos²(A) = 1 - 25/144 = 119/144.

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

cos(A) = - √119/√144 = - √119/12.

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

tan(A) = (5/12) / (- √119/12) = - 5/√119.

Graph :