Chapter 5 Review
1.) If there is an angle in standard position of the measure given, in which quadrant does the terminal side lie?
Quad IIIQuad IV
Quad IIQuad I
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”
3. 5°5’123”
€
52 +25
60= 52.4°
€
−132 −3
60−
45
3600= −132.1°
€
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.
Reference angle is the acute angle formed with the x-axis
And it is always positive!
θ
-150°
θ
€
−19π
18
θ θ
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 = rθ
REMEMBER YOU MUSTBE IN RADIANS
Find the length of each arc. Leave your answer in terms of π
€
s = rθ
REMEMBER YOU MUSTBE IN RADIANS
Find the area of each sector. Round your answers to the nearest tenth.
€
s =1
2r2θ
REMEMBER YOU MUSTBE IN RADIANS
Find the area of each sector. Leave your answer in terms of π
€
s =1
2r2θ
REMEMBER YOU MUSTBE 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
1. sin θ = -2/3 quadrant IV
€
secθ =5
3
sinθ =4
5
cscθ =5
4
tanθ =4
3
cotθ =3
4
€
cscθ =−3
2
cosθ =5
3
secθ =3 5
5
tanθ =−2 5
5
cotθ =− 5
2
€
cosθ =adj
hyp
secθ =hyp
adj
sinθ =opp
hyp
cscθ =hyp
opp
tanθ =opp
adj
cotθ =adj
opp
θ
3
54
θ-2
3
€
5
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:
Find the area of each triangle:
€
Area =1
2ab(sinC)
Area =1
2bc(sinA)
Area =1
2ac(sinB)
Find the area of each triangle:
C
BA
FIRST FIND THE LAST ANGLE BY SUBTRACTING FROM 180
SECOND, DECIDE WHICH OF THE THREE FORMULAS YOU WOULD USE
€
Area =1
2a
2 (sinB)(sinC)
sinA
Area =1
2b
2 (sinA)(sinC)
sinB
Area =1
2c
2 (sinB)(sinA)
sinC
Given two angles and a side
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°
2. a = 5, b = 7, c = 9
3. a = 11.7, b = 13.5, C = 85°20’
4. A = 42°, B = 65°, a = 63
€
Area =1
2(19)2 (sin64°)(sin96°)
sin20°= 471.7
€
s =1
2(5 + 7 + 9) =10.5
Area = 10.5(10.5 − 5)(10.5 − 7)(10.5 − 9) =17.4
€
Area =1
2(11.7)(13.5)sin(85.3°) = 78.1
€
Area =1
2(63)2 (sin65°)(sin96°)
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
2r2(θ − sinθ )
Θ = central angle in radiansr = radius
€
s =1
2(6.9)2 3π
4− sin
3π
4
⎛
⎝ ⎜
⎞
⎠ ⎟
s = 39.3units2
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