Unit Circle Trigonometry Review

Principal Angles and Quadrants

100

Give the principal angle for -10˚

350˚

200

Find the principal angle for -5825˚

295˚

300

Find the principal angle for 89π/17

21π/17 

400

In what quadrant is the angle 103π/15 located?

Q2

500

In what quadrant is the angle 7^C located?

Q 1 (There are ~6.28 radians in a complete circle, so 7^C is QI)

Trig Ratios and the Pythagorean Theorem

100

Find the cosine of pi/4 

sqrt(2)/2

200

Find the tan of the 3pi/4 

-1

300

The one leg of a triangle is 6 inches and the hypotenuse is 8 inches. Find the length of the other leg.

sqrt(28) or 2sqrt(7)

400

The length of one side of a triangle is 2a and the length of the other side is 2a. Find the length of the hypotenuse

2a*sqrt(2) or sqrt(8a^2)

500

The lengths of the legs of a triangle are 24, 26, and 10. Is this a right triangle?

Yes-- 24^2 + 10^2 = 26^2

Converting Between Radians and Degrees

100

What is π/3 in degrees?

60˚

200

What is 5π/4 in degrees?

225˚

300

What is 57π/60 in degrees?

171˚

400

What is 390˚ in radians (as a fraction in simplest form)?

13π/6

500

What is 204˚ in radians (as a fraction in simplest form)?

17π/15

Unit Circle Trig Ratios

100

Evaluate sin( π/4 )

sqrt(2)/2

200

Evaluate cos (11π/6)

sqrt(3)/2

300

Evaluate tan (3π / 4)

-1

400

Evaluate sin (23π/6)

-1/2

500

Evaluate tan (3π/2)

undefined

Reference Angles and Quadrants

100

What is the reference angle of 120^o?

60^o

200

What is the reference angle and quadrant of 5pi/3

pi/3, Q4

300

What is the reference angle and quadrant of 13pi/4

pi/4, Q3

400

How many of these lie on the second quadrant?

-pi/4                       485^o                        -11pi/4

7pi/4                      2345^o                     -1345^o 

4440^o                        95pi/13                   25pi/7

 3

500

What is tan(151pi/3) ?

sqrt(3)