Unit 6: Inverse Circular Functions and Trigonometric Equations

Sec 6.1 - Inverse Circular Functions

100

The domain and range of y=tan^-1(x)

What is D: [-oo,oo], R:(-pi/2,pi/2) ?

200

The exact value of y, without a calculator.

 y=arc cot(-sqrt3) 

What is y=pi/6 ?

300

Evaluate the expression without a calculator.

y=arc csc(-1/2)

What is DNE?  csc can't be equal to   -1/2

400

Evaluate the expression without a calculator.

cos(arctan(-2))

 

1/5

500

Evaluate the expression without a calculator.

 cos(arcsin(3/5)+arccos(5/13))

What is 20/65-36/65=-16/65 ?

Sec 6.2 - Trigonometric Equations I

100

Solve for all exact solutions over 0, 2pi),

without a calculator.

 2cos^2x-sqrt3cosx=0 

 x=pi/2, (3pi)/2,pi/6,(11pi)/6 

200

Solve for all exact solutions over 0, 2pi) , without a calculator.

 -2sin^2x=3sinx+1 

 x=pi/6, (5pi)/6, (3pi)/2 

300

Solve for all exact solutions over 0, 360) , without a calculator.

 (tantheta-1)(costheta-1)=0 

 theta=0,45,225 

400

Solve for all exact solutions over 0, 360) , without a calculator.

2tan^2thetasintheta-tan^2theta=0

 theta=0,30,150,180 

500

Solve for all exact solutions over 0, 360) , without a calculator.

 4cos^2theta+4costheta=-1 

 theta=120,240 

Sec 6.3 - Trigonometric Equations II

100

Solve in radians from  [0,2pi) , without a calculator.

2cos(2x)=-1

 x= (5pi)/6,(7pi)/6

200

Without a calculator, solve in degrees from [0,360).

sinxcosx=1/4

 x=15, 75 

300

Without a calculator, solve in radians from   [0,2pi) .

 cos(2x)+cos(x)=0 

 x=pi/3, pi, (5pi)/3 

400

Without a calculator, solve in radians from   [0,2pi) .

 sin(2x)=2cos^2(x) 

 x=pi/2,(3pi)/2, pi/4, (3pi)/4 

500

CALCULATOR. Solve in radians from [0,2pi).

 tan(2x)-sec(2x)=2 

 x=1.8926, 5.0342

Sec 6.4 - Equations Involving Inverse Trigonometric Functions

100

Without a calculator, solve for exact solutions in radians.

 arc tan(x)=arc cos(5/13) 

 x=12/13 

200

Without a calculator, solve for exact solutions in radians.

 cot^-1x=tan^-1(4/3) 

 x=3/4 

300

Without a calculator, solve for exact solutions in radians.

 arc tan(x)=arc sin(-3/4) 

 x=-(3sqrt7)/7 

400

Without a calculator, solve each equation for exact solutions in radians.

 2cos(2x-pi/4)=sqrt3 

 x=(5pi)/24 

500

Without a calculator, solve each equation for exact solutions in radians.

 tan(3x+pi/6)=1 

 x=pi/36 

Random

100

What color mask does Raphael wear from Teenage Mutant Ninja Turtles?

Red

200

What's the only career that ends in 'j'?

A DJ.

300

What is one of the top two songs on the American top 40 as of May 2, 2026.

Olivia Dean - So Easy (To Fall in Love)

Bruno Mars - I Just Might

400

What were the 3 main Axis powers in WWII?

Germany, Italy and Japan

500

I am a 2-digit number between 60 and 80. My tens digit is 2 more than my ones digit. I am not 64. What number am I?

75