8-4 - 8­4.notebook November 19, 2010 8­4 Relationships...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

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.

Ask a homework question - tutors are online