Midterm 2 Review Sheet: Trigonometry Identities and Equations, Exams of Mathematics

Download Midterm 2 Review Sheet: Trigonometry Identities and Equations and more Exams Mathematics in PDF only on Docsity! Midterm 2 Review Sheet Addition/Subtraction identities for sin and cos: You are supposed to know the addition/subtraction identities of sin(x±y) and cos(x±y). How to express sin 2x and cos 2x in terms of sin x and cos x? How to express sin 4x in terms of sin x and cos x? If sin x = 1 3 and x is in quadrant II, how to find the exact value of sin 4x. The addition/subtraction identities for tan: tan(x + y) = tanx + tan y 1− tanx tan y How to express tan(x + π4 ) in terms of tanx? Double Angle Identities: If sinx = .5 and x is in quadrant I, find the exact value of sin 2x (You need to find the value of cos x). If sin x = .5 (and we don’t know which quadrant x is in), find the exact value of cos 2x. (As cos 2x = 1− 2 sin2 x, we can find the exact value of cos 2x even if we cannot decide the value of cos x! cos x might be negative or positive) Half Angle Identities Given the value of cosx, we may find the value of sin x 2 and cos x 2 (don’t forget the plus/minus!), thus we may find the value of tan x 2 , which is tan x 2 = ± √ 1− cos x 1 + cos x If we know the value of both sinx and cos x, we can find the exact value of tan x 2 (without plus/minus!), that is tan x 2 = 1− cos x sinx 1