Solving Trig Equations

Question

Solve sin(3Θ)=-1/2 for all solutions of Θ in the interval [0,2Π).

 

 

Enter answers in exact radians and in ascending order. Simplify fractions.

Answer 1

sin(3θ) = -1/2

 

Normally, sin(pi/6) = 1/2.  The sine is negative in quadrants III and IV.  pi/6 is the reference angle for pi+pi/6 = 7pi/6 in QIII and 2pi-pi/6 = 11pi/6 in QIV.  So you have:

 

3θ = 7pi/6

 

and

 

3θ = 11pi/6

 

Solve for θ for each equation.