Question

Given that (sin(x) = -4/5) and (x) is in the fourth quadrant, find the value of (cos(90 + x)).

a) (3/5)
b) -(3/5)
c) (4/5)
d) -(4/5)

Answer 1

In the fourth quadrant, the cosine function is negative. The value of cos(90 + x) is (4/5).

Step-by-step explanation:

We are given that sin(x) = -4/5 and x is in the fourth quadrant. In the fourth quadrant, the cosine function is negative. Since we know that sin^2(x) + cos^2(x) = 1, we can solve for cos(x) by substituting the given value of sin(x). sin^2(x) + cos^2(x) = (-4/5)^2 + cos^2(x) = 1. Solving for cos(x), we get cos(x) = 3/5.

To find cos(90 + x), we use the identity cos(a + b) = cos(a)cos(b) - sin(a)sin(b). In this case, a = 90 and b = x. So, cos(90 + x) = cos(90)cos(x) - sin(90)sin(x) = 0cos(x) - 1sin(x) = -sin(x) = -(-4/5) = 4/5.

Therefore, the value of cos(90 + x) is (4/5).