KAYLA :)

This week in class we learned the relationships in trig functions and how to simplify the equations. You can find these relationships on page 317 in the Advanced Math book.

Trig functions can’t cancel out in equations; you have to get them on one side and factor it out!!!!

Pythagorean Relationships:
A.) sin^2 θ + cos^2 θ =1
B.) 1 + tan^2 θ = sec^2 θ
C.) 1 + cot^2 θ = csc^2 θ

Reciprocal Relationships:
A.) csc θ = 1/sin θ
B.) sec θ = 1/cos θ
C.) cot θ = 1/tan θ

Steps- (follow loosely)
A.) Algebra
B.) Identities (try Pythagorean theorem, then move everything to sin and cos if that will help)
C.) Algebra
D.) Continue with 1-3 to end of problem

Example 1: sin^2 X – 1

For this problem all you have to do is look at your Pythagorean Relationships and it’s *sin^2 θ + cos^2 θ =1*, so you subtract one and subtract cos^2 X and your answer would be negative cos^2 X.


Example 2: 1 + tan^2 X

For this problem also, all you have to do is look at your Pythagorean Relationships and it’s *1 + tan^2 θ = sec^2 θ*, so your answer is sec^2 X.