Question

If x is acute, find the value of x that satisfies (5 sin x = 4 cos x).

a) (x = 53.13^∘)
b) (x = 36.87^∘)
c) (x = 26.57^∘)
d) (x = 63.43^∘)

Answer 1

To find the value of x in the equation 5 sin x = 4 cos x, divide both sides by 4 to get sin x = 4/5 cos x. Then, use the identity sin x = tan x * cos x to simplify the equation. Solve for x using the inverse tangent function, and the value of x is approximately 53.13°.

Step-by-step explanation:

To find the value of x that satisfies the equation 5 sin x = 4 cos x, we can use the trigonometric identities. First, divide both sides of the equation by 4 to get sin x = 4/5 cos x. Then, use the identity sin x = tan x * cos x to rewrite the equation as tan x * cos x = (4/5) cos x. Next, divide both sides of the equation by cos x to get tan x = 4/5. Finally, take the inverse tangent of both sides to find the value of x. Using a calculator, we find that x is approximately 53.13°, so the correct answer is option a).