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

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

`\text{ cos(A) = }(4)/(5)`
`\text{ A = }\cos ^(-1)((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.