Trigonometric Identities Putting the Puzzle Pieces Together

Establishing Identities Two functions f and g are said to be identically equal if f(x) = g(x) for every value of x for which both functions are defined. Such an equation is referred to as an identity.

Establishing an Identity Use the basic trig identities to establish the identity csc θ tan θ = sec θ

Guidelines for Establishing Identity 1. Start with the side containing the more complicated expression 2. Rewrite sums or differences of quotients as a single quotient 3. Sometimes, rewriting one side in terms of sines and cosines only will help 4. Always keep your goal in mind. Keep looking at the other side of the equation as you work

Establishing an Identity Establish the identity

Guidelines for Establishing Identities Be careful not to handle like an equation. You cannot establish an identity by such methods as adding the same expression to each side and obtaining a true statement.

Establishing an Identity Establish the identity

Establishing an Identity Establish the identity

Solution

Establishing an Identity Establish the identity

Solution

Establishing an Identity Establish the identity

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Establishing Inverse Trig Identities

Establishing Trig Identities Many more examples on pgs. 478 – 479 On-line examples

Solution

Establishing Inverse Trig Identities Show that

Solution

One Last Toughie Establish the identity