Question

suppose cos(A) = ⅘. use the trig identity sin²(A)+ cos²(A) = 1 to find sin(A) in quadrant IV. round to ten-thousandth

Answer 1

Given the trigonometric functions:

$\text{ cos(A) = }\frac{4}{5}$$\sin ^2(A)+\text{cos}^2(A)\text{ = 1}$

Step 1: Let's first determine the value of A.

$\text{ cos(A) = }\frac{4}{5}$$\text{ A = }\cos ^{-1}(\frac{4}{5})$$\text{ A = 36.8699}^{\circ}$

Step 2: Sin (A) in quadrant IV is negative. Thus, we get:

$\text{ Sin(A) in Quadrant IV = -Sin(A)}$$=-Sin(36.8699^{\circ})$$=\text{ -(0.6000)}$$=\text{ -0.6000}$

Therefore, the answer is -0.6000.