Inverse Trig Fun & Trig Equations Review

Inverse Trig. Fun. 1

100

cos^-1(sqrt(3)/2)

pi/6

200

sin^-1(-sqrt(2)/2)

-pi/4

300

sec^-1(2)

pi/3

400

tan^-1(sqrt(3)/3)

pi/6

500

cot^-1(-sqrt(3))

(5pi)/6

Inverse Trig. Fun. 2

100

sin^-1(sin((9pi)/8))

-pi/8

200

csc(tan^-1(1/2))

sqrt(5)

300

sec(sin^-1((2sqrt(5))/5))

sqrt(5)

400

sin^-1(cos((3pi)/4))

-pi/4

500

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

(2pi)/3

Linear Trig. Equations

400

Find all solutions in the interval  0≤theta<2pi 

cos(theta/3-pi/4)=1/2

(7pi)/4

500

Find all solutions in the interval  0≤theta<2pi 

sin(3theta+pi/18)=1

theta={(4pi)/27,(22pi)/27,(40pi)/27}

Quadratic Trig. Equations

300

Find all solutions in the interval  0≤theta<2pi 

(cot theta+1)(csc theta - 1/2)=0

theta={(3pi)/4,(7pi)/4}

400

Find all solutions in the interval  0≤theta<2pi 

2cos^2 theta - 7 cos theta - 4 =0

theta={(2pi)/3,(4pi)/3}

500

Find all solutions in the interval  0≤theta<2pi 

2sin^2 theta=3(1-cos(-theta))

theta={0,pi/3,(5pi)/3}

Inverse Trig. Fun. 3

300

cos(tan^-1 u)

1/sqrt(u^2+1)

400

sin(cos^-1 u))

sqrt(1-u^2)

500

tan(sec^-1 u))

usqrt(1-1/u^2)