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8-4 - 8­4.notebook 8­4 Relationships among the functions...

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Unformatted text preview: 8­4.notebook November 19, 2010 8­4 Relationships among the functions. I. Reciprocal relationships sinθ = 1/cscθ cosθ = 1/secθ tanθ = 1/cotθ cotθ = 1/tanθ secθ = 1/cosθ cscθ = 1/sinθ II. Also tanθ = sinθ/cosθ cotθ = cosθ/sinθ III. Relations with negatives sin (­θ) = ­sin (θ) cos (­θ) = cos (θ) tan (­θ) = ­tan (θ) cot (­θ) = ­cot(θ) sec (­θ) = sec (θ) csc (­θ) = ­csc (θ) Mar 20­8:19 AM IV. Pythagorean relations sin2θ + cos2θ = 1 1 + tan2θ = sec2θ 1 + cot2θ = csc2θ V. Cofunction Relations sin θ = cos (900 ­ θ) cos θ = sin (900 ­ θ) tan θ = cot (900 ­ θ) cot θ = tan (900 ­ θ) do activity 1 p. 318 sec θ = csc (900 ­ θ) csc θ = sec (900 ­θ) Mar 20­9:06 AM 1 8­4.notebook November 19, 2010 Put everything into sin θ or cos θ Simplify each expression Ex. 1 sin θ sec θ cot θ Ex. 2 sec x - sin x tan x class ex. p. 320 1­7 p. 321 1­12 Apr 2­1:23 PM Simplifying complex fractions. Ex. t + (1/t) t Ex. tan x + (1/tan x) tan x Apr 2­1:27 PM 2 8­4.notebook November 19, 2010 Ex. a b 1 ­ 1 a b Ex. sec x ­ tan x cos x cot x Apr 2­1:31 PM Ex. y + x x y 1 xy Ex. sin x + cos x cos x sin x 1 sin x cos x Apr 2­1:35 PM p. 321 13­24 3 8­4.notebook November 19, 2010 Proving identities Ex. 1 + 1 = ­2cot2x 1 ­ sec x 1 + sec x Ex. cot x(1 + tan2 x) = csc2 x tan x p. 322 29­36 Apr 2­1:41 PM 4 ...
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