Find the solutions

Question

Find the solutions of the equation that are in the interval [0, 2𝜋). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

sin(2t) − sin(t) = 0

Answer 1

Since sin(2t) is identical to 2 sintcost the equation can be written as:

2sin(t)cos(t - sin(t) = 0;

No factor out sin(t) to get:

sin(t) [2cos(t) -1]=0..

By the zero product theorem:

sin(t) = 0 OR 2cos(t) - 1 = 0.

That means t = sin^-1(0) OR t = cos^-1(1/2)

From the first we have t = 0, t = π.

From the 2nd t = π/3 , t = 5π/3.

Use the graph to verify:

desmos.com/calculator/l3kzaoalmp