Expert: Sherry Wallin - 10/29/2009

Question
Use a graphing utility to approximate the solutions of the equation in the interval [0, 2π). If possible, find the exact solutions algebraically. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)
sin(2x) + cos(x) = 0

Approximate solutions:
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2.
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5.
6.

Exact solutions (in terms of π):
1.
2.
3.
4.
5.
6.


I've tried so  many steps by writing the original equation first then doing the double angle formula i factor it out set factors equal to zero but it keeps saying i'm getting the wrong solution please kindly help me. My friend Lisa recommend me to you :)

thank you


Answer
sin(2x) + cos(x) = 0 note this implies that sin 2x = - cos x. You could always change - cos x into -sin (90-x) so you have sin 2x = -sin (90-x). Now take arcsin of both sides getting 2x = -(90-x) = x-90
Ok so now you have 2x = x - 90 so x = -90, now put that value back into the original equation:
sin(2(-90)0 = sin (-180) = 0 and cos (-90)= 0

I can't do the calculator partfor you, you will need to explore that on your own. You should be able to see on the graph where these two functions sin 2x and -cos x are opposites so that their difference is 0.

Math Prof