Question

Solve the equation 8 sin x = 2.5 for
the interval 0° to 720°

Answer 1

18.2°, 161.8° and 378.2°

Explanation:

Given the expression:

8 sin x = 2.5

Divide both sides by 8

sinx = 2.5/8

Sinx = 0.3125

x = arcsin(0.3125)

x1 = 18.2

Since sin theta is positive in the second quadrant, x2 = 180 - 18.2 = 161.8°

Since our angle must lie in between 0° and 720°,then;

x3 = 360 + 18.2 = 378.2°

Hence the required angles are 18.2°, 161.8° and 378.2°