# Thread: Need help on solving Trig equations

1. ## Need help on solving Trig equations

Hello,
I am taking a precalc class and am having trouble when it comes to solving trig equations. Our book does not do a very good job on explaining and I have been unable to find any examples or similar problems to the following:
find all solutions ofin the interval [0,2pie) x representing theta.
sin(x)cos(3x)+cos(x)sin(3x)=0

cos(x)+sin(x)=0

cos(x/2)-1=2

2sin^2(x)=sin(x)

cos(2x)=sin(x)

cos(2x)=squareerootof 2 -cos(2x)

If anyone could explain the steps and how to solve these it would be greatly appreciated.

2. Originally Posted by ConfusedMath
Hello,
I am taking a precalc class and am having trouble when it comes to solving trig equations. Our book does not do a very good job on explaining and I have been unable to find any examples or similar problems to the following:
find all solutions ofin the interval [0,2pie) x representing theta.
sin(x)cos(3x)+cos(x)sin(3x)=0

note the pattern ... sin(a)cos(b)+cos(a)sin(b) = sin(a+b)

cos(x)+sin(x)=0

this is just general knowledge of the unit circle ... at what angles does cos(x) = -sin(x) ??

cos(x/2)-1=2

cos(x/2) = 3

what is the range of cos(anything) ?

2sin^2(x)=sin(x)

2sin^2(x) - sin(x) = 0

factor and solve

cos(2x)=sin(x)

1 - 2sin^2(x) = sin(x)

0 = 2sin^2(x) + sin(x) - 1

factor and solve

cos(2x)=squareerootof 2 -cos(2x)

2cos(2x) = sqrt(2)

cos(2x) = sqrt(2)/2

look at your unit circle

...

3. Thank you so much!!