Calculus Test 2

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tanO/2=

(1-cosO)/sinO

Evaluate: tan(cos-1(x/2))

(4-x^2)r/x

assuming Q1 cos(tan-1(x))

(x^2+1)r/x^2+1

cosO/2 =

+/- (1+cosO/2)r

sinO/2=

+/- (1-cosO/2)r

sin(sin-1(x)) = x if

-1<O<1

tan-1(tan-3pi/8)

-3pi/8

tan-1 (-infinity)

-pi/2

tan-1(tan(x)) = x if

-pi/2 < O < pi/2

unit circle sin-1(cos2pi/3) =

-pi/3

tan-1(cos(pi))

-pi/4

sin-1(sin7pi/6)

-pi/6

cos^2(x)+sin(x)+1 = 0

3pi/2

tan-1(tan(3pi/7))=

3pi/7

cos(sin-1(1/2))

3r/2

sin(cos-1(3/5) + tan-1(12/5))

56/65

evaluate: cos(sin-1(-2/3))

5r/3

y=3sin(-2x) period and amplitude

A: 3 P: pi (pi,0)

fd exact value cos(75)cos(15)+sin(75)sin(15)

cos(60)=1/2

tan-1(2)

defined, but not on the unit circle

cos -1(-1)

pi

sin-1(sin4)

pi-4

cos-1(cos(-5pi/3))

pi/3

sin-1(sin2pi/3)

pi/3

tan-1(tan8pi/7)

pi/7

fd exact value tan(75)-tan(15)

tan(60)=3r

tan-1(sin(3pi/2)/cos(pi/2))

tan-1 = -1/0 = undefined = tan-1(-infinity) = -pi/2

cos-1(pi)

undefined

sin(sin-1(pi/2))

undefined

sin-1(pi/2)

undefined

sin-1(sinx)

x

trig func sin(4x)=-1

x = 3pi/8, 7pi/8, 11pi/8, 15pi/8

trig func 2cosxsinx-cosx=0

x=pi/2, 3pi/2, pi/6, 5pi/6

trig func sin(4x)=1

x=pi/8, 5pi/8, 9pi/8, 13pi/8

tan(2x)=1

x=pi/8, 7pi/8, 11pi/8, 15pi/8

Definition of O=cos^-1 (y)

y=cosO y=0<O<pi

Definition of O=tan^-1(y)

y=tanO y=pi/2 < O < pi/2

cos(3x)=1/2

...

2sin(x)+tan(x)=0

0, 2pi/3, pi, 4pi/3

sin(tan-1(infinity))

1

cos-1(cos2)

2

evaluate: tan(15)

2-3r

sin(sin-1(2/3)) =

2/3

cos-1 (-1/2)

2pi/3

cos-1(sin (pi/6) + tan (3pi/4))

2pi/3

cos-1(sin(7pi/6))=

2pi/3

Sin2O =

2sinO (cosO)

tan2O=

2tanO/1-tan^2O

sin(sin-1(x)-cos-1(x)))

2x^2-1

cosO=4/5 Q1, simplify sin (O+pi/3)

3+4(3r)/10

fd and simply csc(15)

6r+2r

Fd and simply sin(15)

6r-2r/4

y=5cos(pix) period and amplitude

A: 5 P: 2 (2,5)

y=5cos(-2x) period and amplitude

A: 5 P: pi (pi, 5)

y=5tan(1/4x) period and amplitude

A: none P: 4pi (-2pi, 2pi)

cos-1(cosx)=x if

O<x<pi

Cos2O =

cos2O-sin^2O 2cos^2O -1 1-2sin^2O

tan^2(x)=sec(x)+1

pi/3,pi,5pi/3

cos -1 (2r/2)

pi/4

tan-1(1)

pi/4

cot(x) = 2cos(x)

pi/6, pi/2, 5pi/6, 3pi/2

sin-1(sin(pi/7)=

pi/7

sin(sin-1(2) =

undefined sin-1(>1) = undefined


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