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”

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52 +25

60= 52.4°

€

−132 −3

60−

45

3600= −132.1°

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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.

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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

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secθ =5

3

sinθ =4

5

cscθ =5

4

tanθ =4

3

cotθ =3

4

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cscθ =−3

2

cosθ =5

3

secθ =3 5

5

tanθ =−2 5

5

cotθ =− 5

2

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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

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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

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Area =1

2(19)2 (sin64°)(sin96°)

sin20°= 471.7

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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.

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s =1

2r2(θ − sinθ )

Θ = central angle in radiansr = radius

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s =1

2(6.9)2 3π

4− sin

3π

4

⎛

⎝ ⎜

⎞

⎠ ⎟

s = 39.3units2