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Pre-Cal

Pre-Cal. Chapter 5 Analytical Trigonometry Section 5.1 Fundamental Identities. Definitions. Identities: different ways to write trig functions but that actually have the same value. Basic Trig Identities. Reciprocal Identities: csc x = 1/sin x sec x = 1/cos x cot x = 1/tan x

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Pre-Cal

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  1. Pre-Cal Chapter 5 Analytical Trigonometry Section 5.1 Fundamental Identities

  2. Definitions • Identities: different ways to write trig functions but that actually have the same value.

  3. Basic Trig Identities • Reciprocal Identities: • csc x = 1/sin x • sec x = 1/cos x • cot x = 1/tan x • sin x = 1/csc x • cos x = 1/sec x • tan x = 1/cot x • Quotient Identities: • tan x = sin x / cos x • cot x = cos x / sin x

  4. Pythagorean Identities • cos2 x+ sin2 x = 1 • 1 + tan2 x = sec2 x • cot2 x + 1 = csc2 x

  5. Cofunction Idendtities • sin ( π/2 – x ) = cos x • cos ( π/2 – x ) = sin x • tan( π/2 – x ) = cot x • cot ( π/2 – x ) = tan x • sec ( π/2 – x ) = csc x • csc ( π/2 – x ) = sec x

  6. Odd-Even Identities • sin(-x) = -sin x • cos(-x) = cos x • tan(-x) = -tan x • csc(-x) = -csc x • sec(-x) = sec x • cot(-x) = -cot x

  7. Simplifying Trig Identies • To simplify the different Trig Identities you must factor and/or replace pieces in order to cancel out as much information as possible. • You will have to factor a lot from here on out. You factor trig the same way you factor any other equations.

  8. Using Identities to Solve Equations • You will be using the Pythagorean Identities, Quotient Identities, and Reciprocal Identities. • Plug in what you know and use the appropriate identities to solve for what is asked for.

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