precal question

Question

Use an Addition or Subtraction Formula to simplify the equation.

sin(𝜃) cos(3𝜃) + cos(𝜃) sin(3𝜃) = 0

𝜃 = 

Find all solutions in the interval [0, 2𝜋). (Enter your answers as a comma-separated list.)

𝜃 = 

Answer 1

Using the addition formula we can simplify the equation into

sin(4θ) = 0

Therefore

4θ = kπ for any integer k

θ = kπ/4

In the interval [0,2π) the following value are of the above form:

0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4