Tool: Verifying trig identities (see p. 441). An
identity is an equation that should be true for all values of θ . If it is, then
you can use the identities you already know to simplify both
sides to be equal to each other.
Tool: Trig equations are true only for certain
values of an
angle ( unlike identities , which are true for all values ).
Always be aware of restrictions. They will tell you where to
look for solutions when you apply inverse trig functions.
Tool: Reference triangles can help you find
solutions of trig equations.
Tool: Known solutions and 30-60-90, 45-45-90
Tool: Factoring and finding zeros of factors may
solutions. Think back to when you factored quadratics , but
now we have trig functions.
Tool: Trig identities can be used to solve. You may
Simplifying trig expressions:
Verifying Trig identities for all angular values:
Proving an equation is not an identitiy:
Practice with cosine sum and difference formulas:
Compute the following exactly (no decimal).
Cofunction identity practice:
What is sec(90−θ)?
Evaluate the expression exactly (no decimal): Hint: recognize the proper identity to simplify
Evaluate the expression exactly (no decimal):
Hint: inverse trig functions output angles. Use triangles
find those angles.
(optional)Practice: You don't really need to
of sum and difference angle formulas because you can use
even-odd properties to derive one from the other.
Derive the formula for tan(u+v) using even-odd
identities for tangent.
Evaluating trig functions.
Let θ be a first quadrant angle such that tan(θ)= 5/12 .
Compute exactly (no decimal).
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