1.) If there is an angle in standard position of the measure given, in which quadrant does the terminal side lie?
Quad III
Quad IV
Quad I
Quad II

2.) Change angle measure to radian measure in terms of π, or degree measure
Degrees to radians
π/180
Radians to degrees
180/π

4.) Change the given angle to a degree measure rounded to the nearest tenth.
1. 52°25’
2. -132°3’45”

52

25
60

52.4


132

3
60

45
3600
 
132.1

3. 5°5’123”

5

5
60

123
3600

5.1



5.) Find the reference angle for each angle.
Reference angle is the acute angle formed with the x-axis
And it is always positive

5.) Find the reference angle for each angle.
θ
θ
-150°

θ

19

18
θ
Reference angle is the acute angle formed with the x-axis
And it is always positive!

Find a positive and a negative coterminal angle for each given angle.
ADD 2π
OR
SUBTRACT 2π

Find the measure of each angle in red using the green angle given.

Find the length of each arc. Round your answers to the nearest tenth.
s
 r

REMEMBER YOU MUST
BE IN RADIANS


Find the length of each arc.
Leave your answer in terms of π s
 r

REMEMBER YOU MUST
BE IN RADIANS


Find the area of each sector. Round your answers to the nearest tenth.
s

1
2 r
2

REMEMBER YOU MUST
BE IN RADIANS


Find the area of each sector.
Leave your answer in terms of π s

1
2 r
2

REMEMBER YOU MUST
BE IN RADIANS


I will give you one trig function’s value, and I will tell you in which quadrant the terminal sides lies,
YOU TELL ME THE 5 OTHER TRIG FUNCTIONS.
1. cos θ = 3/5 quadrant I cos
  adj hyp sec
  hyp adj
1. sin θ = -2/3 quadrant IV csc
 

3
2
5
θ
3
4 sec
 
5
3 sin
 
4 csc
 
5
5
4 tan
 
4
3 cot
 
3
4 sin
  opp hyp csc
  hyp opp tan
  opp adj cot
  adj opp

3
θ
5
-2 cos
 
3
5 sec
 
3 5
5

2 5 tan
 
5

5 cot
 
2
  

Find the exact value, WITHOUT USING A
CALCULATOR!

Solve each triangle. Round answers to the nearest tenth.
Use your trig ratios
And Pythagorean theorem

Solve each triangle. Round answers to the nearest tenth.
Use your trig ratios
And Pythagorean theorem

18.) Use the Law of Sines to solve each triangle.
Round your answers to the nearest tenth.

Use the Law of Cosines and solve the triangle complety:

Area

1
2 ab (sin C )
Area

1
2 bc (sin A )
Area

1
2 ac (sin B )



C
Given two angles and a side FIRST FIND THE LAST ANGLE BY
SUBTRACTING FROM 180
SECOND, DECIDE WHICH OF THE THREE
FORMULAS YOU WOULD USE
A
Area

1
2 a
2
(sin B )(sin C ) sin A
Area

1
2 b
2
(sin A )(sin C ) sin B
Area

1
2 c
2
(sin B )(sin A ) sin C
B

Find the area of the triangle with sides 31, 44, and 60 units:
GIVEN THREE SIDES = HERO’S FORMULA

Find the area of each triangle:
1. A = 20°, a = 19, C = 64°
Area

1
2
(19)
2
(sin 64

)(sin 96

) sin 20


471.7
1. a = 5, b = 7, c = 9
 s

1
2
(5

7

9)

10.5
Area

10.5(10.5

5)(10.5

7)(10.5

9)

17.4
2. a = 11.7, b = 13.5, C = 85°20’

3. A = 42°, B = 65°, a = 63
Area

1
2
(11.7)(13.5)sin( 85.3

)

78.1
 Area

1
2
(63)
2
(sin 65

)(sin 96

) sin 42


2570.5


28.) Find the area of a circular segment to the nearest tenth if the measure of its central angle is
135° and the measure of its radius is 6.9 units.
 s

1
2 r
2
(
  sin

)
Θ = central angle in radians r = radius s

1
2
(6.9)
2 
3
4

 sin
3

4
 s

39.3
units
2
