8-4

8-4 is on the relationships among trig functions.
There are several formulas you need to know for this section:

• Cscx=1/sinx
• Secx=1/cosx
• Cotx=cosx/sinx
• Tanx=sinx/cosx
• sin^2x+cos^2x=1
• 1+tan^2x=sec^2x
• 1+cot^2x=csc^2x
• sinx=cos(90 degrees - theta)
• tanx=cot(90 degrees - theta)
• secx=csc(90 degrees - theta)
• cosx=sin(90 degrees - theta)
• cotx=tan(90 degrees - theta)
• cscx=sec(90 degrees - theta)

Steps:
1. Algebra
2. Identities - try pythagorean theorem then move everything to sin and cos.
3. Algebra
4. Continue with steps 1-3

Ex. 1 sin^2x(1+cot^2x)
1. Algebra: You can't do any algebra with this problem.
2. Identities: You can use one of your pythagorean theorems. So you end up with sin^2x(csc^2x).
3. Algebra: You still can't do any algebra with this problem.
4. Steps 1-3: Now you can change csc^2x to 1/sin^2x. That gives you sin^2x(1/sin^2x). Now you can cancel out the sin^2x leaving you with 1. So your answer is 1.

Ex. 2 sinx/cosxtanx
1. Algebra: You can't do any algebra with this problem.
2. Identities: You can change tanx to sinx/cosx. So you get sinx/cosx(sinx/cosx).
3. Algebra: You can cancel out the cosx leaving you with sinx/sinx.
4. Steps 1-3: Your final answer is 1.

Amber :)