Question

Which of the following is a solution to sin(2x) - cos x=0

A.) 60°
B.) 90°
C.) 120°
D.) 240°
E.) 300°

Answer 1

The solution to the equation sin(2x) - cos x = 0 is x = 30° or x = 150°. The correct answer is option C.) 120°

Step-by-step explanation:

We are given the equation sin(2x) - cos x = 0. To find the solutions, we need to solve for x. Let's rewrite the equation in terms of sin and cos functions:

sin(2x) = cos x

Using the double angle identity for sine, we have:

2sin x cos x = cos x

Dividing both sides by cos x, we get:

2sin x = 1

Dividing both sides by 2:

sin x = 1/2

The standard angles where sin has the value of 1/2 are 30° and 150°. However, since we want the solutions for 2x, we need to double these values:

2x = 60°, 300°

Dividing both sides by 2:

x = 30°, 150°

Therefore, the solution to the equation sin(2x) - cos x = 0 is x = 30° or x = 150°.