Ch. 5 Review

Definition

100

cosine

x/r or x/1

200

tangent

y/x

300

secant

r/x or 1/x

400

cosecant 

r/y or 1/y

500

cotangent

x/y

Trig Identity

100

tangent

sin(x)/cos(x)

200

cotangent

cos(x)/sin(x)

300

sin(-x)

-sin(x)

400

sin²(x) + cos²(x)

1

500

tan²(x)

sec²(x)-1

Solve Trig Equation

100

-2sin(x) + 1 = 0

x = pi/6 + 2pi n , 5pi/6 + 2pi n

200

sqrt (3) csc(x) - 2 = 0 

x= pi/3 + 2pi n , 2pi/3 + 2pi n

300

cos³(x) - cos(x) = 0

x = 0 + 2pi n , pi + 2pi n

400

2sin²(x) + 3sin(x) + 1 = 0

x = 7pi/6 + 2pi n, 11pi/6 + 2pi n, 3pi/2 + 2pi n

500

2sin(x/2) + sqrt(3) = 0 in [0 , 4pi)

x = 8pi/3 , 10pi/3

Simplify Trig

100

sin(x)cos²(x)-sin(x)

-sin³(x)

200

(sec²(x)-1)/sec²(x)

sin²(x)

300

1/(1-sin(x)) + 1/(1+sin(x))

2sec²(x)

400

(cos(x)cot(x))/(1-sin(x)) - 1 

csc(x)

500

cos(x) - (cos(x)/(1-tan(x)))

(sin(x)cos(x)/(sin(x)-cos(x))

Inverse Trig

100

sin^-1(-1/2)

-pi/6

200

cos(-2)

DNE

300

tan^-1(-1)

-pi/4

400

cos(sin^-1(-3/5))

4/5

500

cos^-1(sin(-pi/4))

3pi/4