Question

Sin(3theta) = -1

Solve each equation on the interval 0 ≤ θ< 2π

Answer 1

Solve for theta:
sin(3 theta) = -1
Eliminate the sine from the left hand side by taking the inverse sine of both sides:

3 theta = 2 pi n-pi/2 for n element Z

Solve for theta.

Divide both sides by 3

Answer:
theta = (2 pi n)/3-pi/6 for n element Z; n=0 and n=1

There are 2 other solutions, can you figure these out?

Answer 2

pi/6 and 5pi/6?

Answer 3

@chaise
Isn't the value of theta limited to the given interval?

Answer 4

Yes, the values of n=0 and n=1 will give values in between the interval.