2 sin(2𝜃) = 1. Find the solutions in the interval [0, 2𝜋).

Answer 1

Madison,

I would first recommend setting your expression equal to theta. This can be accomplished through the inverse trigonometric identities. Your expression should come out looking something like:

θ = (1/2)arcsin(1/2)

This tells us that we are looking for the locations on the unit circle where the angle is half of pi/6 and 5pi/6, which you can find by asking yourself where the sine function is equal to 1/2 on the unit circle.This means your answers should be:

pi/12 and 5pi/12

Answer 2

Divide both side by 2 and solve.