Homework Help: Trig.

Posted by mary on Saturday, February 27, 2010 at 8:55pm.

Can someone please help me with this?
Find all solutions to the equation in the interval [0,2pi)
cos2x=sinx

I know I have to use some sort of identity, but I have no idea how to go about to solve this.

Trig. - MathMate, Saturday, February 27, 2010 at 9:25pm
Yes, by making use of the identity
cos2x = cos²x-sin²x=1-2sin²x, the given equation can be transformed to:
2sin²x+sinx-1=0
which is a quadratic in sin(x).
Solving the quadratic by factoring,
(2sinx-1)(sinx+1)=0
or sin(x)=1/2 or sin(x)=-1
Find all roots in the interval [0,2π].
Trig. - mary, Saturday, February 27, 2010 at 10:14pm
Thank you very much for the help
Trig. :) - MathMate, Sunday, February 28, 2010 at 8:16am
You are welcome!

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