8-4 (and no bad algebra)

This week we learned about relationships among trig functions…how riveting. The first thing you will need to know is your Pythagorean Identities.

Sin^2Ɵ+cos^2Ɵ=1, tan^2Ɵ+1=sec^2Ɵ, cot^2Ɵ=csc^2Ɵ

Now, the following steps are to be loosely followed.

1. Algebra (In this step you should factor, FOIL, etc. oh and don’t do it badly.)

2. Identities (first you will want to try one of the Pythagoreans I listed earlier. If none of these work move everything to sin and cos if that helps)

3. ALGEBRA :D but don’t do it badly.

4. Continue with steps 1-3, but no bad algebra.

It may also help you to look back over some algebra to save yourself some time while doing these sorts of problems.

Now, time for the example :D

Solve.

(sinƟ-1)(sinƟ+1)

The first thing you want to do here is FOIL (without bad algebra).

Sin^2Ɵ-1

Next, you’ll want to check your Pythagorean identities and, lucky for me, this is one! In the margin, write that sin^2Ɵ+cos^2Ɵ=1

Subtract sin^2Ɵ from both sides and you will discover your answer is cos^2Ɵ.

Oh and don't forget, no bad algebra.

--Sarah