Question

An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 2 sin(2θ) = 1 (a) Find all solutions of the equation. θ = (b) Find the solutions in the interval [0, 2π). θ =

Answer 1

Answer:

a) θ = 15° b) θ = 15°, 165°

Step-by-step explanation:

a) Given the equation 2 sin(2θ) = 1

sin(2θ) = 1/2

(2θ) = arcsin(1/2)

2θ = 30°

θ = 15°

b) To find all the solutions between 0 and 2π, we will make reference to the quadrant.

Sinθ is positive in the first and second quadrant.

In the first quadrant, θ = 15°

In the second quadrant, θ = 180°-15°

= 165°

The solutions between 0 and 2π are 15° and 165°