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Pre Calc Chapter 7. Analytic Trig. Trigonometric Identities—7.1. Analytic Trigonometry. Reciprocal Identities Pythagorean Identities. Analytic Trigonometry. Even-Odd Identities Co-function Identities. Even-Odd Identities. Why does sin(-x) = -sin(x)??. Co-Function Identities.
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Pre Calc Chapter 7 Analytic Trig
Analytic Trigonometry • ReciprocalIdentities • PythagoreanIdentities
Analytic Trigonometry • Even-Odd Identities • Co-function Identities
Even-Odd Identities Why does sin(-x) = -sin(x)??
Proving Identities • Prove one side equals the other • Usually* try to modify the more difficult side • If stumped try working other side • Generally don’t want to “meet in the middle”
Addition and Subtraction Identities • Proving Co-Function Identities
Sums of Sines and Cosines • If A and B are real numbers, then: where and
Sums of Sines and Cosines • Express the function in terms of sine only
Sums of Sines and Cosines • Express the function in terms of sine only
Half-Angle Formulas The choice of + or – depends on the quadrant of x/2
Product to Sum Formulas • Re-write the following product as a sum
Product to Sum Formulas • Find the value of the following
Sum to Product Formulas • Re-write the following sum as a product
Sum to Product Formulas • Find the value of the following
Inverse Trig Functions • What is an inverse function? • If f is one-to-one function with domain A and range B, then its inverse is a function with domain B and range A
Inverse Trig Functions • Inverse sine function (arcsine)
Inverse Trig Functions • Examples:
Inverse Trig Functions • Inverse Cosine
Inverse Trig Functions • Examples
Inverse Trig Functions • Inverse Tangent