Solving Trig Equations

When solving trigonometric equations, there are two things to consider:

1) You may need to square both sides in order to solve it.

2) Checking for extraneous solutions is necessary in some cases.

Squaring Both Sides

It may be necessary to square both sides of the equation in order to solve it. For example, if left with something like 1+ cosx=sinx, there are no other options.

1 + cosx = sinx

1 + cos^2x = sin^2x *Square both sides.

1 + cos^2x= 1 - cos^2x *Substitute the pythagorean identity.

cos^2x = -cos^2x *Subtract 1 from both sides.

2cos^2x= 0 *Add cos^2x to both sides.

cosx = 0 * Divide by 2 and take the square root of both sides.

x = π/2, 3π/2 *Use unit circle knowledge to find angles

and now....

We must check for extraneous solutions!

When is this required?

1) Anytime you square both sides of the equation.

2) To make sure the denominator is not 0.

For #1, plug in you're answers to make sure it remains true.

For #2, plug in answers to the denominator, and make sure it just does not equal 0.