Thread: sin(x - pi/3) = 0

1. sin(x - pi/3) = 0

"The Humongus Book of Trigonometry Problems" (by Kelley) has the problem

sin (x - pi/3) = 0

as one of their "Advanced Trigonometric Equations". After a bunch of steps, the answers for between 0 and 2*pi as:

pi/3, 2pi/3, 4pi/3, 5pi/3

How can 2pi/3 be a solution? I plug in and get sin(pi/3) and that is not zero. A similar problem with 5pi/2.

2. Re: sin(x - pi/3) = 0

Originally Posted by duckey123
"The Humongus Book of Trigonometry Problems" (by Kelley) has the problem
sin (x - pi/3) = 0 as one of their "Advanced Trigonometric Equations". After a bunch of steps, the answers for between 0 and 2*pi as:
pi/3, 2pi/3, 4pi/3, 5pi/3 How can 2pi/3 be a solution? I plug in and get sin(pi/3) and that is not zero. A similar problem with 5pi/2.

$\displaystyle \sin \left( {\frac{\pi }{3} - \frac{\pi }{3}} \right) = 0\quad ,\;\sin \left( {\frac{{4\pi }}{3} - \frac{\pi }{3}} \right) = 0$

3. Re: sin(x - pi/3) = 0

Where did 2pi/3 and 5pi/3 come into play?

4. Re: sin(x - pi/3) = 0

Originally Posted by duckey123
Where did 2pi/3 and 5pi/3 come into play?
Nowhere! There are only two solutions. See HERE.