5.1 Fundamental Identities

An identity is an equation that is true for every value in the domain of its variable.

Fundamental Identities

Reciprocal Identities

Quotient Identities

Pythagorean Identities

Negative-Angle Identities

Note: Alternate forms are also useful as

Using the Fundamental Identities to find additional trig values

Example

If is in quadrant IV, use appropriate identities to find the function values.

a) sin θ b) tan θ c) sec(-θ)

NOTE: When taking square roots, be careful to choose the appropriate sign.
Using the Fundamental Identities to express one function in terms of another

Any trig function of a number or angle can be expressed in terms of any other function!!!

Example

Express in terms of

Example

Write in terms of , and then simplify the expression.

Note: When working with trig expression and identities, be sure to write the argument of the function. That is, do not write - and correct your teacher if she does it!!!