Trig Equations

Unit Circle Review

100

sin((7pi)/6)

-1/2

200

cos((3pi)/4)

-sqrt2/2

300

tan(pi/4)

1

400

tan((2pi)/3)

-sqrt3

Unit Circle Backwards

100

Find all values in [0,2pi) that make the equation true.

sintheta=1/2

theta=pi/6,(5pi)/6

200

Find all values in [0,2pi) that make the equation true.

costheta=-1

theta=pi

300

Find all values in [0,2pi) that make the equation true.

tantheta=1

theta=pi/4,(5pi)/4

400

Find all values in [0,2pi) that make the equation true.

sintheta=-sqrt2/2

theta=(5pi)/4,(7pi)/4

Simple Trig Equations

100

Find all values in [0,2pi) that make the equation true.

sin^2theta-1=0

theta=pi/2,(3pi)/2

200

Find all values in [0,2pi) that make the equation true.

2costheta+sqrt2=0

theta=(3pi)/4,(5pi)/4

300

Find all values in [0,2pi) that make the equation true.

tantheta-sqrt3=0

theta=pi/3,(4pi)/3

400

Find all values in [0,2pi) that make the equation true.

4cos^2theta-1=0

theta=pi/3,(2pi)/3,(4pi)/3,(5pi)/3

Trig Equations and Factoring

100

Find all values in [0,2pi) that make the equation true.

sinthetacostheta+sintheta=0

theta=0,pi

200

Find all values in [0,2pi) that make the equation true.

sqrt3sintheta+2sinthetacostheta=0

theta=0, pi,(5pi)/6,(7pi)/6

300

Find all values in [0,2pi) that make the equation true.

2cos^2theta+3costheta+1=0

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

400

Find all values in [0,2pi) that make the equation true.

2sin^2theta+sintheta-1=0

theta=pi/6,(5pi)/6,(3pi)/2

Surprise!

100

Find all values in [0,2pi) that make the equation true.

2costheta+1=0

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

200

Find all values in [0,2pi) that make the equation true.

4sin^2theta-3=0

theta=pi/3,(2pi)/3,(4pi)/3,(5pi)/3

300

Find all values in [0,2pi) that make the equation true.

costheta+cos^2theta=0

theta=pi/2,(3pi)/2,pi

400

Find all values in [0,2pi) that make the equation true.

tan^2theta+tantheta=0

theta=0,pi,(3pi)/4,(7pi)/4