Unit 4 Review

What is 60 degrees in radians? 

• 2π/3

• π/3

• 4π/3

• π/6

Answer explanation

To convert degrees to radians, use the formula: radians = degrees × (π/180). For 60 degrees: 60 × (π/180) = π/3. Thus, the correct answer is π/3.

Tags

CCSS.HSF.TF.A.1

What is 45 degrees in radians?

• π/2

• π/6

• π/4

• 3π/4

Answer explanation

To convert degrees to radians, use the formula: radians = degrees × (π/180). For 45 degrees: 45 × (π/180) = π/4. Thus, 45 degrees is π/4 radians.

Tags

CCSS.HSF.TF.A.1

What is 3π/4 radians in degrees?

• 315

• 135

• 150

• 330

Answer explanation

To convert radians to degrees, use the formula: degrees = radians × (180/π). For 3π/4 radians, it becomes (3π/4) × (180/π) = 135 degrees. Thus, the correct answer is 135.

Tags

CCSS.HSF.TF.A.1

What is the co-terminal angle of -80⁰ ?

• -10⁰

• -280⁰

• 10⁰

• 280⁰

Answer explanation

To find a co-terminal angle, add 360° to -80°. This gives -80° + 360° = 280°. Therefore, the co-terminal angle of -80° is 280°.

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.4

What is the co-terminal angle of 210⁰ ?

• -30⁰

• -150⁰

• -40⁰

• 150⁰

Answer explanation

To find a co-terminal angle, subtract or add 360°. For 210°, subtracting 360° gives -150°. Thus, -150° is the correct co-terminal angle.

Tags

CCSS.HSF.TF.A.4

Which quadrant is 2π/3 in?

• I

• II

• III

• IV

Answer explanation

The angle 2π/3 radians is in the second quadrant because it is between π/2 (90 degrees) and π (180 degrees). In this quadrant, the x-coordinates are negative and the y-coordinates are positive.

Tags

CCSS.HSF.TF.A.2

Which of the following is closest to the measure of the angle drawn by the green curve?

• 5/6 π

• 5/3 π

• 4/5 π

• 4/3 π

Answer explanation

The angle drawn by the green curve is closest to 5/3 π, which represents an angle of 300 degrees. This is larger than 5/6 π (150 degrees) and 4/5 π (144 degrees), but less than 4/3 π (240 degrees).

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.4

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

• 7/10 π

• 3/8 π

• 7/20 π

• 3/2 π

Answer explanation

The angle closest to the measure shown is 7/10 π, which is approximately 2.2 radians. This is more accurate compared to the other options, making it the correct choice.

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.1

CCSS.HSG.C.B.5

When the rotation from initial to terminal side is counterclockwise this describes. 

• Positive Angle

• Negative Angle

Answer explanation

When the rotation from the initial to the terminal side is counterclockwise, it indicates a positive angle. Therefore, the correct answer is 'Positive Angle'.

Tags

CCSS.HSF.TF.A.2

CCSS.HSG.CO.A.4

Find the length s of the arc that subtends a central angle of measure 40° in a circle of radius 12 m.

• 8.38 m

• 480 m

• 3.3 m

• 10.2 m

Answer explanation

To find the arc length s, use the formula s = r * θ (in radians). Convert 40° to radians: θ = 40° * (π/180) = 2π/9. Then, s = 12 m * (2π/9) ≈ 8.38 m. Thus, the correct answer is 8.38 m.

Tags

CCSS.HSG.C.B.5