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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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This note was uploaded on 04/22/2011 for the course MATH 212 taught by Professor Owens during the Winter '07 term at Grand Valley State University.
- Winter '07