Chapter 4: Circular Functions

Review for Lessons 1 & 2

Mrs. Parziale

• A windshield wiper on a car turns through an angle of 100°. The blade is 14 inches and the arm is 10 inches. How much of an area does the blade cover, to the nearest tenth?

10”

14”

How Much Plastic Is Needed?

5 10 cm

• James needs to replace the plastic covering his speedometer on his old car. If the needle can maximally rotate 105, find the area of the piece of plastic he will need. Find your answer to the nearest tenth.

Find the Area of the Sector

• The circle to the right has a radius of 6 inches. The line shown has an equation of y = x. Find the exact area of the shaded sector.

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y

Calculate Arc Length

• Given radius and central angle

2

34radius inches

67radius inches

Calculate area of a sector

• Given radius and central angle

2

34radius inches

67radius inches

Convert to degrees

3

2revolutions CCW

314revolutions CW

4

7revolutions CCW

Convert to degrees

3

2radians 3

2radians

5

6radians

Convert to revolutions

5

6radians

10

3radians

15

6radians

Calculate Arc Length

• Given radius and central angle

Calculate area of a sector

• Given radius and central angle

Convert to degrees

54𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠𝐶𝐶𝑊

136𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠𝐶𝑊

Convert to radians

56𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠𝐶𝐶𝑊

154𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠𝐶𝑊

Convert to degrees (two dec)

76𝑟𝑎𝑑𝑖𝑎𝑛𝑠

7𝜋6𝑟𝑎𝑑𝑖𝑎𝑛𝑠

Convert to revolutions (fraction)

450 ° 315 °

Calculate Exact Value• Convert degrees to radians – leave in terms of

200

60

300

• The length of the arc of a circle is inches. • The measure of its central angle is 33° . – Convert 33° to radians– What is the exact radius of the circle?

5

12

r

• Find the length of an arc with radius 5 meters and central angle radians. Give your answer exactly.

3

Find the Radius

• If a sector of a circle with a central angle of has an area of 6.4 square meters, what is the length of the radius?

5

Find the Angle Measure

• If a sector of a circle with radius of 14 cm has an area of 256.56 square meters, what is the measure of the central angle in degrees? (round answer to the nearest degree)

• A windshield wiper on a car turns through an angle of 150°. The blade is 12 inches and the arm is 5 inches. How much of an area does the blade cover, to the nearest tenth?

5”

12”