Solve the equation sin3x=0.5, [-pi,pi]

Question

Is the answer pi/18, 13pi/18, -11pi/18, 5pi/18, 17pi/18 and -7pi/18?

Answer 1

Hi Edward,

 

You are looking for solutions on the interval x ∈ [-π, π], so 3x ∈ [-3π, 3π]

 

sin(3x) = 0.5

 

This occurs at reference angles of π/6 in the first and second quadrants.

3x = π/6, 5π/6

 

You're interested in the solutions up to ±3π, so you also have

3x = π/6, 5π/6

3x = π/6 + 2π, 5π/6 + 2π

 = 13π/6, 17π/6

3x = π/6 - 2π, 5π/6 - 2π

 = -11π/6, -7π/6

 

Divide these all by 3 to get

x = π/18, 5π/18, 13π/18, 17π/18, -11π/18, -7π/18

 

Your answers are correct. Good job!

Answer 2

The sin(30deg)= 0.5, so 3x= 30deg, and x= 10deg.