8-4 Relationships Among Functions

This week I am going to teach you how to solve problems by using relationships among trig functions. This section can look extremely intimidating. Do not worry about it. After you do a few problems, you will get the hang of it. There are a multitude of formulas that you can use to help you evaluate these problems. Here is a list of the formulas:
Reciprocal Relationship Formulas:
csc(theta)=1/sin(theta) sec(theta)=1/cos(theta) cot(theta)=1/tan(theta)
tan(theta)=sin(theta)/cos(theta) cot(theta)=cos(theta)/sin(theta)
Pythagorean Relationship Formuals:
sin^2(theta)+cos^2(theta)=1 1+tan^2(theta)=sec^2(theta) 1+cot^2(theta)=csc^2(theta)
Cofunction Relationship Formulas:
sin(theta)=cos(90 degrees-theta) and cos(theta)=sin (90 degrees-theta)
tan(theta)=cot(90 degrees-theta) and cot(theta)=tan (90 degrees-theta)
sec(theta)=csc(90 degrees-theta) and csc(theta)=sec (90 degrees-theta)

The steps are as follows:
(Follow these loosely)
1. Algebra
2. Identities(try Pythagorean first, then change everything to sin and cos if it helps)
3. Algebra
4. Continue with steps 1-3
Examples:
1. (1-cosx)(1+cosx)
• 1+cosx-cosx-cos^2(x)
• 1-cos^2(x)
• sin^2(x)
2. (1-cosx)(1+secx)cosx
• (1-cosx)(1+1/cosx)cosx
• 1+(1/cosx)-cos-(cos/cos)
• 1+(1/cosx)-cosx-1
• (1/cosx)-cosx
• (1/cosx)-(cos^2/cos)
• (1-cos^2/cos)
• (sin^2/cos)
-Braxton