Solving Trig Equations Int: [0,2pi]

Inverse Trig

100

acrsin(root3/2)

pi/3

200

arctan(-1)

-pi/4

300

arccos(-1/(2^1/2)) 

(-1 over root 2) 

3pi/4

400

DOUBLE JEOPARDY

arcsin(0)

0

500

arctan(-(3^1/2))

(- root 3)

-pi/6

Isolate and Solve

100

2sin(x)=2

x=pi/2

200

sec²(x)=2

x=pi/4, 3pi/4, 5pi/4, 7pi/4

300

4cos²(x)-1=0

pi/3, 5pi/3

400

3sin(x)=-1

x₁=-.34 or 5.943

x₂=2.802

500

sin²(x)=0.3249

ALL QUADRANTS: 

x₁=0.607

x₂=2.535

x₃=3.748

x₄=5.677

Solve by Factoring

100

tan²(x)+tan(x)=0

x= 0, pi, 3pi/4, 7pi/4

200

sin²(x)=sin(x)

x=0, 2pi, pi, -3pi/2

300

2cos²(x)-cos(x)=1

x=0, 4pi/3, 2pi/3

400

DOUBLE JEOPARDY

cos²(x)-3cos(x)=-2

x=3pi/2

500

2cos²(x)-cos(x)-3=0

x=pi

Composition

100

sin(acrsin(-1/2))

-1/2

200

arccos(cos(7pi/6))

5pi/6

300

tna(arccos(-(root 3)/2)

-1/root 3

400

sin(arccos(6/9))

root(45)/9

500

tan(arccos(-3/x))

root(x²+9)/-3

Good Info to Know

100

sin(x) and csc(x) are what? 

Reciprocal functions of each other

200

Cos(x) and Arccos(x) are what? 

Inverse fucntions of each other

300

What is the range of sin(x)?

[-1,1]

400

What is the range of: 

a. arcsin(x)

b. arccos(x)

c. arctan(x)

a. [-pi/2, pi/2]

b. [0, pi]

c. [-pi/2, pi/2]

500

What is the domain of: 

a. sin(x)

b. cos(x)

All real numbers 

(-Inf., Inf)