How do you solve sin(3x)= -1 with domain between 0 and 2pi?

2 Answers
May 17, 2015

sin 3x = -1 = sin ((3pi)/2) -> 3x = (3pi)/2 -> x = pi/2.

Check: When x = pi/2 -> 3x - = (3pi)/2 -> sin 3x = -1 OK

Sin 3x= -1 would have us 3x= (3pi)/2 and also (3pi)/2 +2pi and (3pi)/2+4pi

x= pi/2, pi/2+(2pi)/3, pi/2+(4pi)/3

x=pi/2, (7pi)/6, (11pi)/6

These are the three solution for x in 0<=x<=2pi

Nov 10, 2015

Solve sin 3x = - 1

Ans: pi/2; (7pi)/6; (11pi)/6 for (0, 2pi)

Explanation:

Trig Table of Special Arcs and trig unit circle -->
sin 3x = - 1 = sin ((3pi)/2) --> 3x = (3pi)/2 + 2kpi -->

x = pi/2 + (2/3)kpi
- If k = 0 --> x = pi/2
- If k = 1 --> x = pi/2 + (2pi)/3 = (7pi)/6
- If k = 2 --> x = pi/2 + (4pi)/3 = (11pi)/6