PreCalculus Chapter 5 Review

Trig Identities

100

simplify cotxsecx

cscx

200

simplify

(1-sin^2x)/(csc^2x - 1)

sin²x

300

Simplify 

tan^4x+2tan^2x+1

sec⁴x

Verifying Identities

100

Show that tant*cott = 1

tan = sin/cos and cot = cos/sin

200

show that 

sin^2alpha - sin^4alpha = cos^2alpha - cos^4 alpha

factor out sin² on the left. use sin² + cos² = 1 to go from there. 

300

Show that 

tanx/(1-cos^2x) = secxcscx

use tanx = sinx/cosx and 1-cos²x = sin²x 

Solving Trig Equations

100

2cos(x/2) = -1

x = (2pi)/3 or (4pi)/3

200

2sin^2x + 3sinx + 1 = 0

factor to get sinx = -0.4 or -1 . . . so 

x = (7pi)/6, (11pi)/6, or (3pi)/2

300

sqrt(3)sectheta + secthetacottheta=0

theta = (5pi)/6 or (11pi)/6

Sum and Diff Formulas**

100

Find sinx and tanx if cosx = -3/5; 

pi < x< (3pi)/2

sinx = -4/5 and tanx = 4/3

200

Find cosy and siny if tany = -5/12; 

(-pi)/2 <y<0

cosy = 12/13

siny = -5/13

300

Need sum/diff 100 and 200 first!!

Find sin(x + y) if cosx = -3/5

pi<x<(3pi)/2

 and tany = -5/12 

-pi/2 <y<0

sin(x + y) = -33/65

Double and Half Angle Formulas**

100

Need answer for sum/difference 100 first!!

find tan(x/2)

-2

200

Need answer for sum/diff 100 first!!

Find cos2x

-7/25

300

solve for x: 4sinxcosx = 1

rewrite with double angle formula 2sin2x = 1. Solve for

2x = pi/6 and (5pi)/6

 --> 

x = pi/12 or (5pi)/12