Unit 1

Degrees <-> Radians

100

150^o

5𝛑/6

200

𝛑/3

60^o

300

-520^o

-26𝛑/9

400

-41𝛑/12

-615^o

500

-105^o

-7𝛑/12

Coterminal Angles, Arc Length, and Sector Area

100

Find at least one positive coterminal angle to -1140^o

300^o

200

Find a positive AND negative coterminal angle to 3𝛑

𝛑 and -𝛑

300

What are the equations for arc length and sector area?

s=(^𝜃/_2𝛑)(2𝛑r)=r𝜃

area=(^𝜃/_2𝛑)(𝛑r²)=¹/₂r²𝜃

400

A circle has a radius of 6 and a central angle of 48^o. What is the arc length?

First turn the angle from degrees to radians=48(^𝛑/₁₈₀)=^48𝛑/₁₈₀=^12𝛑/₄₅

Then solve for arc length=s=6(^12𝛑/₄₅)=^8𝛑/₅

500

A sector with an angle of ^𝛑/₆ and a radius of 12 cm. What is the sector area?

a=¹/₂(12)²(^𝛑/₆)

a=¹/₂(144)(^𝛑/₆)

a=(72)(^𝛑/₆)

a=^72𝛑/₆

a=12𝛑cm²

Trig Ratios

100

What are the 3 basic trig rations?

sin=^opposite/_hypotenuse

cos=^adjacent/_hypotenuse

tan=^opposite/_adjacent

200

If you have the adjacent of an angle and the hypotenuse, which trig ratio would you use to solve for the opposite?

cos

300

For angle x the opposite side is 12, the adjacent side is 5, and the hypotenuse is 13. Find cos(x).

cos=⁵/₁₃

400

An angle of 70^o has a hypotenuse of 5. Solve for the adjacent side(x).

cos(70)=^x/₅

5cos(70)=x

1.71=x

500

An angle of 65^o has an adjacent side of 3, solve for the hypotenuse(x).

cos(65)=³/_x

x(cos(65))=3

x=³/_cos(65)

x=7.092

Exact Values

100

Find the exact value of sin(^-𝛑/₄)

^-√2/₂

200

Find the exact value of cos(^25𝛑/₃)

¹/₂

300

Find the exact value of tan(^-3𝛑/₄)

1

400

Find the exact value of sec(^5𝛑/₃)

2

500

Find the exact value of csc(^15𝛑/₂)

-1

Inverse Trig Functions

100

What are the 3 inverse trig functions?

sin^-1(^opposite/_hypotenuse)=𝜃

cos^-1(^adjacent/_hypotenuse)=𝜃

tan^-1(^opposite/_adjacent)=𝜃

200

Solve cos(cos^-1(¹/₂))

cos(cos^-1(x))=x if -1 ≤ x ≤ 1

Therefore the answer is ¹/₂

300

Solve sin^-1(-¹/₂)

-^𝛑/₆

400

Solve tan^-1(1)

^𝛑/₄

500

Solve sin(sec^-1(¹³/₅))

¹²/₁₃