Trigonometry Honors Chapter 6

6.1 Day 1 and 2Inverse Trigonometric Functions

100

The degree measure of θ if  θ=arcsin(-√2/2)

-45 degrees

200

The degree measure of θ if θ=arcsec(-2)

θ=120 degrees

300

The function value of sin(arccos 1/4)

√15 / 4

400

The function value tan(arccos u) as a non-trigonometric expression in u 

√(1-U²) / U

500

The function value of cos(2arctan 4/3) using the double angle identity

-7/25

6.2 Day 1 and 2 Trigonometric Equations I

100

The solutions of 2tan(x)= 3sin(x) in the interval [0°,360°) using a calculator to the nearest tenth of a degree

x= 48.2°, 180°, 311.8°, 0°

200

The solution of the trigonometric equation: 

2sin²x - sinx-1 = 0 by factoring in the interval [0, 2𝛑)

X= 7𝛑/6 , 11𝛑/6 , 𝛑/2

300

The solutions of the equation in the interval [0°, 360°) by squaring : sin² (x)cos² (x)=0 

X= 0°, 90°, 180°, 270°

400

Find the approximate solutions to the nearest hundredth by factoring in the interval [0,2𝝅) : 

tan² x-4=0

x= 2.03, 5.17,1.12, 4.25

500

The exact solution in the interval [0°, 360°) using the quadratic formula : 

4cos²X + 4cosX =1

281.95°

6.3Trigonometric Equations II

100

The double angle identity of sin

sin(2x)=2sin(x)cos(x)

200

The exact solution in the interval [0°, 360°) of the equation: sin x/2 =1

X=180°

300

The exact solutions in the interval [0°, 360°) of the equation: cos 2x = -1/2

x= 60°,120°,240°,300°

400

The exact solutions in the interval [0°, 360°) of the equation: sinxcosx=1/4

x=15°,75°,195°, 225°

500

The exact solutions in the interval [0°, 360°) of the equation: sin2x=2cos²x

x=90°,270°,45°,225°

6.4 Day 1 and 2 Equations Involving Inverse Trigonometric Functions

100

The value of the variable x in the equation: 4y=sinx

(solve for x)

arcsin(4y)=x 

200

Solve arccos(y-𝝅/3)= 𝝅/6

((3√3)+(2𝝅)) / 6

300

The value of the variable x in the equation :

 arcsin x = arctan(4/3)

x=4/5

400

Find the value of x using an identity in the equation: arcsinx+arctan√3=2𝝅/3

x=√3/2

500

Find the value of x in the equation : 

arcsinx + arctanx=0 

x=0

Information about inverse functions

100

The range and domain of y=arcsinx

range:[-1,1]

domain: [-𝛑/2,𝛑/2]

200

The quadrant(s) of the unit circle from which range values come for y=arccsc(x)

Quadrants I and IV

300

The range and domain of y=arccos(x)

range: [0,𝛑]

domain: [-1,1]

400

The domain and range of y=arcsec(x)

Domain : (-∞,-1]U[1,∞)

Range: [0, 𝛑/2)U(𝛑/2,𝛑]

500

The quadrants of the unit circle from which range values come for y=arccot(x)

Quadrants I and II