Question

How do you solve the equation 9 sin (x - 15°) = -4? The answer is 221.4° and 348.6°. How do you get this answer?

a) x = 25.6° and x = 40.4°
b) x = 211.4° and x = 348.6°
c) x = -221.4° and x = -348.6°
d) x = 15.0° and x = 60.0°

Answer 1

To solve the equation 9 sin (x - 15°) = -4, you need to isolate the angle x and use the inverse sine function to find its value. The solutions are approximately 221.4° and 348.6°.

Step-by-step explanation:

To solve the equation 9 sin (x - 15°) = -4, we need to isolate the angle x.

1. First, divide both sides of the equation by 9 to get sin (x - 15°) = -4/9.
2. Next, take the inverse sine of both sides to find x - 15°. This gives us x - 15° = sin-1(-4/9).
3. Finally, add 15° to both sides to solve for x. This gives us x = sin-1(-4/9) + 15°.

Using a calculator, we can find that x is approximately 221.4° and 348.6°.