Solving absolute values of trigonometry

[Physics53]

Homework Statement

Homework Equations

The Attempt at a Solution

2sin3x=1 OR 2sin3x= -1
sin3x=1/2 sin3x= -1/2
From the unit circle and in accordance with the domain
there are 3 solutions (B)
But the answer is (C)
HOW?

 

[Ray Vickson]

Homework Statement

View attachment 229661

Homework Equations

The Attempt at a Solution

2sin3x=1 OR 2sin3x= -1
sin3x=1/2 sin3x= -1/2
From the unit circle and in accordance with the domain
there are 3 solutions (B)
But the answer is (C)
HOW?

In your problem, $\theta = 3x$ runs from $\theta = 0$ to $\theta = 3 \pi.$ Look at a plot of $y = \sin \theta$ for $0 \leq \theta \leq 3 \pi.$ How many places are there at which $\sin \theta = 1/2$ or $\theta = -1/2?$