Free Printable Trigonometry 10

Worksheets

Trigonometry 10

Total questions: 48

Worksheet time: 36mins

Name

Class

Date

Which of the following statements is true about angles drawn in standard position?

The terminal side is the side of the angle that is initially drawn.

The initial side is the side of the angle that is initially drawn.

The terminal side is the side of the angle that intersects the positive x-axis after rotation.

The initial side is the side of the angle that intersects the positive x-axis after rotation.

Which of the following statements correctly describes negative and positive angles?

Positive angles are measured in a counterclockwise direction from the initial side, while negative angles are measured in a clockwise direction.

Positive angles are measured in a clockwise direction from the initial side, while negative angles are measured in a counterclockwise direction.

Both positive and negative angles are measured in a clockwise direction from the initial side.

Both positive and negative angles are measured in a counterclockwise direction from the initial side.

Which of the following pairs of angles are coterminal?

45 and 135

60 and −300

90 and 270

180 and −180

What is the measure, in radians, of a central angle that intercepts an arc equal in length to the radius of the circle?

𝜋 radians

𝜋/2 radians

1 radians

2𝜋 radians

Which of the following angles lie on the axes and are considered quadrantal angles?

30°

60°

90°

120°

Which of the following best defines an acute angle in radians?

An angle whose measure is greater than 𝜋/2 radians.

An angle whose measure is exactly 𝜋/2 radians.

An angle whose measure is less than 𝜋/2 radians.

An angle whose measure is exactly 𝜋 radians.

Which of the following best defines an obtuse angle in radians?

An angle whose measure is greater than 𝜋/2 radians.

An angle whose measure is exactly 𝜋/2 radians.

An angle whose measure is less than 𝜋/2 radians.

An angle whose measure is exactly 𝜋 radians.

Which of the following angles does not have a supplementary angle?

𝜋/3

𝜋/2

𝜋/4

3𝜋/2

Which formula accurately converts an angle from degrees to radians?

𝑅𝑎𝑑𝑖𝑎𝑛𝑠=180/𝜋×𝑑𝑒𝑔𝑟𝑒𝑒𝑠

𝑅𝑎𝑑𝑖𝑎𝑛𝑠=𝜋/180×𝑑𝑒𝑔𝑟𝑒𝑒𝑠

𝑅𝑎𝑑𝑖𝑎𝑛𝑠=90/𝜋×𝑑𝑒𝑔𝑟𝑒𝑒𝑠

𝑅𝑎𝑑𝑖𝑎𝑛𝑠=𝜋/90×𝑑𝑒𝑔𝑟𝑒𝑒𝑠

10.

Which formula accurately converts an angle from radians to degrees?

𝐷𝑒𝑔𝑟𝑒𝑒𝑠=180/𝜋×𝑟𝑎𝑑𝑖𝑎𝑛𝑠

𝐷𝑒𝑔𝑟𝑒𝑒𝑠=𝜋/180×𝑟𝑎𝑑𝑖𝑎𝑛𝑠

𝐷𝑒𝑔𝑟𝑒𝑒𝑠=90/𝜋×𝑟𝑎𝑑𝑖𝑎𝑛𝑠

𝐷𝑒𝑔𝑟𝑒𝑒𝑠=𝜋/90×𝑟𝑎𝑑𝑖𝑎𝑛𝑠

11.

What is the measure of 3𝜋/2 in degrees?

240°

270°

300°

330°

12.

What is the supplement of an angle measuring 𝜋/3?

𝜋/6

𝜋/2

2𝜋/3

𝜋

13.

Given a circle with radius 𝑟=5 units, if a central angle 𝜃 intercepts an arc of length 𝑠=10 units, what is the measure of 𝜃 in radians?

1 radians

3 radians

2 radians

5 radians

14.

Which formula accurately calculates the arc length 𝑠 intercepted by a central angle 𝜃 in a circle of radius 𝑟?

𝑠=𝜃/𝑟

𝑠=𝑟𝜃

𝑠=𝑟/𝜃

𝑠=𝜃+𝑟

15.

What formula accurately calculates the linear speed 𝑣 of a particle moving at a constant speed along a circular arc of radius 𝑟, where 𝑠 is the length of the arc traveled in time 𝑡

𝑣=𝑟/𝑡

𝑣=𝑠/𝑡

𝑣=𝑡/𝑠

𝑣=𝑡/𝑟

16.

A car is traveling along a circular track with a radius of 100 meters. If it covers an arc length of 200 meters in 20 seconds, what is the linear speed of the car?

5 m/s

10 m/s

15 m/s

20 m/s

17.

Which formula accurately calculates the angular speed 𝜔 of a particle moving at a constant speed along a circular arc, where 𝜃 is the angle (in radians) corresponding to the arc length 𝑠, and 𝑡 is the time taken to cover the arc?

𝜔=𝑠/𝑡

𝜔=𝑡/𝑠

𝜔=𝜃/𝑡

𝜔=𝜃/𝑠

18.

A ceiling fan has blades that are 80 centimeters long. The fan rotates at 10 revolutions per second. Determine the angular speed of the fan in radians per second.

20 𝜋 radians/second

10 𝜋 radians/second

5𝜋 radians/second

2𝜋 radians/second

19.

A pizza parlor offers a special deal where you can buy a pizza with a sector angle of 33π radians. If the pizza has a radius of 12 inches, what is the area of this sector?

198π square inches

198 square inches

2376 square inches

2,376π square inches

20.

What formula accurately calculates the area 𝐴 of a sector of a circle, given the radius 𝑟 and the central angle 𝜃 in radians?

$A=r^2\theta$

$A=\frac{1}{2}r^2\theta$

$A=\frac{r^2}{\theta}$

$A=\frac{1}{2}r\theta$

21.

Convert the angle 48.75° to degree-minute-second form.

48°45′0′′

48°45′30’′

48°27′0′′

48°27′30′′

22.

What is 5π/6 radians in degrees?

180

150

360

120

23.

What is 11π/6 radians in degrees?

330

360

300

24.

What is 225 degrees in radians?

7π/4

5π/4

3π/4

5π/3

25.

How many radians does a circle have?

360 degrees

2\pi radians

$\pi radians$

^{2 radians}

26.

Find an angle coterminal with an angle which measures 11π ∕ 3.

17 π / 3

4π ∕ 3

π ∕ 3

8π ∕ 3

27.

Which of the following is closest to the measure of the angle shown?

30º

40º

395º

440º

28.

In a circle with a diameter of 24 cm, a central angle of $\frac{4\pi}{3}$ radians intercepts an arc. The length of the arc, in terms of $\pi$ , is

$16\pi$

$4\pi$

$3\pi$

$32\pi$

29.

In circle O, the length of radius is 9 centimeters and the area of sector AOB is $\frac{27\pi}{2}$ square centimeters. The measure of in radians is

$\frac{\pi}{3}$

$3\pi$

$\frac{1}{3\pi}$

$\frac{3}{\pi}$

30.

What is the area of a sector of a circle with a radius of 8 inches and formed by a central angle that measures $\frac{\pi}{3}$ ?

$\frac{8\pi}{3}$

$\frac{16\pi}{3}$

$\frac{32\pi}{3}$

$\frac{64\pi}{3}$

31.

Find the area of the shaded sector.

5.2

7.9

10.5

15.7

32.

In a circle with a diameter of 24 cm, a central angle of $\frac{4\pi}{3}$ radians intercepts an arc. The length of the arc, in terms of $\pi$ , is

$16\pi$

$4\pi$

$3\pi$

$32\pi$

33.

What are the negative and positive coterminal angles of 240 degrees?

540°, -120°

600°, -120°

425°, -240°

120°, -135°

34.

Calculate the length of an arc with radius 15 cm and central angle of 30°.

450 cm

5π/2 cm or ≈ 7.9 cm

225 cm

5π/4 cm or ≈ 3.9 cm

35.

Calculate the area of a sector with central angle of 140° and radius of 8 cm.

224/9 cm² or ≈ 24.9 cm²

896 π/9 cm² or ≈ 312.8 cm²

4480 cm²

224 π/ 9 cm² or ≈ 78.2 cm²

36.

Determine the central angle if the arc length is 10 cm and the radius is 5 cm.

2°

not possible ... "s" is too small

≈ 114.6°

360°

37.

A ceiling fan with 16 inch blades rotates at 45 rpm. Find the angular velocity of the fan in rad/min. Round to the nearest tenth.

90 rad/min

282.7 rad/min

45 rad/min

141.4

38.

A car tire has a diameter of 14 inches and is spinning at a of 10 revolutions per second. What is the linear speed in miles per hour?

7.95π mi / 1 hr

15.90 mi / 1 hr

3.28 rad / 1 hr

2.84 rad / 1 hr

39.

A car tire has a diameter of 14 inches and is spinning at a rate of 10 revolutions per second. What is the angular speed in radians per hour?

120π rad / 1 hr

1,008,000π rad / 1 hr

504,000π rad / 1 hr

7200π rad / 1 hr

40.

Find the angle generated by point P in time when r = 20 cm, w=pi/12 per sec and t = 6 sec.

Pi/2

pi/12

41.

Find the linear speed of P when r = 30 cm, w= pi/10 per sec and t = 4 sec.

pi/10

2 pi

3 pi

pi/2

42.

A bicycle traveled a distance of 100 meters. The diameter of the wheel of this bicycle is 40 cm. Find the number of rotations of the wheel.

20 rotations

40 rotations

65 rotations

80 rotations

43.

Determine the linear velocity of the tips of the blades in inches per minute for a ceiling fan with 20 inch blades rotating at 45 rpm.

5654.9 in/min

1800 in/min

2827.4 in/min

900 in/min

44.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.

9.2 sq. in.

10.5 sq. in.

31.4 sq. in.

38.2 sq. in.

45.

Convert 150⁰ to radians

5π/6

3π/4

7π/6

2π/3

46.

Angle 280 is in

quadrant 1.

quadrant 2.

quadrant 3.

quadrant 4.

47.

Find a coterminal angle to 45 degrees.

360

405

315

295

48.

What is the reference angle for 240 degrees?

60 degrees

30 degrees

45 degrees

210 degrees

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Trigonometry 10

Total questions: 48

Worksheet time: 36mins

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