Calculus 1000A/B Lecture Notes - Lecture 3: Inverse Function

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Pei Yu

Document Summary

We continue our review of trigonometry and the discussion about inverse trigono- metric functions. f (x) = sin x f (x) = cos x f (x) = tan x. 2 -periodicity of sin x and cos x: sin(x + 2 ) = sin x, cos(x + 2 ) = cos x for all x. Periodicity of tan x: tan(x + ) = tan x, for x 6= . Also sin( x) = sin x, cos( x) = cos x, tan( x) = tan x sin(x + Rewrite, using that sec x = 1 cos x : (tan x)2 + 1 = (sec x)2. Half-angle formulas: sin(2x) = 2 sin x cos x cos(2x) = (cos x)2 (sin x)2. Two other helpful identities: sin(x + y) = sin x cos y + cos x sin y cos(x + y) = cos x cos y sin x sin y.