8 4 relationships among the functions
15
8.4 Relationships Among the Functions Objectives: 1. Simplify trig expressions 2. Prove trig identities
description
Transcript of 8 4 relationships among the functions
8.4 Relationships Among the Functions
Objectives:
1. Simplify trig expressions
2. Prove trig identities
Relationships with Negatives
If P is a point onthe unit circle, then x = cos θand y = sin θ.
Pythagorean Identities
Since P(cos θ, sin θ) is on the unit circle:
We’ll verify these later!
To Simplify:
Use trig identities to try to express as one trig function or as a constant.
It often helps to rewrite everything in terms of sine and cosine.
Example:
Simplify the expression.
Example:
Simplify the expression.
Example:
Simplify:
You Try!
Simplify each expression:
Investigating Cofunctions
Use your calculator to evaluate:
sin 50° cos 40°
sin 25° cos 65°
sin 79° cos 11°
sin 7° cos 83°What do you notice?
Why Does This Happen?
Cofunction Relationships
Proving Identities
Simplify one (or both) side(s) of the equation to show they are equal.
Need to work with each side separately. Don’t move anything across the = sign.
Example:
Prove:
Example:
Prove:
You Try!
Prove:
