for Whoobee's shop
Grade 11 Quiz: Trigonometry — Easy Version 1
Grade 11 · Whoobee Name: ____________________ Date: __________
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.
How to solve
This quiz mixes questions from different lessons, like a real test. Read each question carefully: the lesson name in front tells you what kind of problem it is. Check your answers, then practise the lessons where you made mistakes.
Example
Radians, Arc Length & Sector Area: Convert 2π radians to degrees.
Answer: 360
Not quite. The answer is
💡 The highest points of the graph are at y = 5 and the lowest at y = -1. The amplitude is half the distance between them: (5 − (-1)) ÷ 2 = 6 ÷ 2 = 3.
✓ Correct!
Not quite. The answer is
💡 The highest points of the graph are at y = 5 and the lowest at y = -1. The amplitude is half the distance between them: (5 − (-1)) ÷ 2 = 6 ÷ 2 = 3.
💡 How to solve: Amplitude, Period & Midline of Sine and Cosine
For y = a sin(bx) + d or y = a cos(bx) + d: the amplitude is |a|, the period is 2π ÷ b, and the midline is y = d. The maximum value is d + |a| and the minimum is d - |a|. On a graph, the amplitude is half the distance from a maximum to a minimum, and the period is the horizontal length of one full cycle.
Try a similar one
Find the amplitude of y = -3cos(x) - 4.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Multiply by 180/π: 3π/4 × 180/π. The π cancels, leaving 3 × 180 ÷ 4 = 540 ÷ 4 = 135°.
✓ Correct!
Not quite. The answer is
💡 Multiply by 180/π: 3π/4 × 180/π. The π cancels, leaving 3 × 180 ÷ 4 = 540 ÷ 4 = 135°.
💡 How to solve: Radians, Arc Length & Sector Area
To change degrees to radians multiply by π/180; to change radians to degrees multiply by 180/π. With the angle θ in radians, the arc length is s = rθ and the sector area is A = (12)r2θ.
Try a similar one
Convert 45° to radians: 45° = ___π
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Subtract 360° once: 620° − 360° = 260°. The angle is 260°.
✓ Correct!
Not quite. The answer is
💡 Subtract 360° once: 620° − 360° = 260°. The angle is 260°.
💡 How to solve: Coterminal & Reference Angles (Degrees & Radians)
Coterminal angles end in the same place: add or subtract 360° (or 2π) until the angle is in the range you want, e.g. 430° - 360° = 70° and -110° + 360° = 250°. The reference angle is the acute angle between the terminal side and the x-axis: in quadrant I it is θ, in II it is 180° - θ, in III it is θ - 180°, and in IV it is 360° - θ (use π and 2π for radians). For an angle outside 0° to 360°, find its coterminal angle first.
Try a similar one
Find the angle between 0° and 360° that is coterminal with 600°.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 In y = a sin(bx) + d, a = -2, b = 4 and d = -4. The amplitude is |a| = |-2| = 2.
✓ Correct!
Not quite. The answer is
💡 In y = a sin(bx) + d, a = -2, b = 4 and d = -4. The amplitude is |a| = |-2| = 2.
💡 How to solve: Amplitude, Period & Midline of Sine and Cosine
For y = a sin(bx) + d or y = a cos(bx) + d: the amplitude is |a|, the period is 2π ÷ b, and the midline is y = d. The maximum value is d + |a| and the minimum is d - |a|. On a graph, the amplitude is half the distance from a maximum to a minimum, and the period is the horizontal length of one full cycle.
Try a similar one
Find the amplitude of y = 2cos(4x) - 4.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use s = rθ: s = 11 × 3π/4 = 33π/4, so the answer is 334.
✓ Correct!
Not quite. The answer is
💡 Use s = rθ: s = 11 × 3π/4 = 33π/4, so the answer is 334.
💡 How to solve: Radians, Arc Length & Sector Area
To change degrees to radians multiply by π/180; to change radians to degrees multiply by 180/π. With the angle θ in radians, the arc length is s = rθ and the sector area is A = (12)r2θ.
Try a similar one
Convert 135° to radians: 135° = ___π
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 150° is between 90° and 180°, so it is in quadrant II. In quadrant II the reference angle is 180° − θ = 180° − 150° = 30°.
✓ Correct!
Not quite. The answer is
💡 150° is between 90° and 180°, so it is in quadrant II. In quadrant II the reference angle is 180° − θ = 180° − 150° = 30°.
💡 How to solve: Coterminal & Reference Angles (Degrees & Radians)
Coterminal angles end in the same place: add or subtract 360° (or 2π) until the angle is in the range you want, e.g. 430° - 360° = 70° and -110° + 360° = 250°. The reference angle is the acute angle between the terminal side and the x-axis: in quadrant I it is θ, in II it is 180° - θ, in III it is θ - 180°, and in IV it is 360° - θ (use π and 2π for radians). For an angle outside 0° to 360°, find its coterminal angle first.
Try a similar one
Find the angle between 0° and 360° that is coterminal with 580°.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 In y = a cos(bx) + d, a = 3, b = 4 and d = -2. The period is 2π ÷ b = 2π ÷ 4 = π/2, so the answer is 12.
✓ Correct!
Not quite. The answer is
💡 In y = a cos(bx) + d, a = 3, b = 4 and d = -2. The period is 2π ÷ b = 2π ÷ 4 = π/2, so the answer is 12.
💡 How to solve: Amplitude, Period & Midline of Sine and Cosine
For y = a sin(bx) + d or y = a cos(bx) + d: the amplitude is |a|, the period is 2π ÷ b, and the midline is y = d. The maximum value is d + |a| and the minimum is d - |a|. On a graph, the amplitude is half the distance from a maximum to a minimum, and the period is the horizontal length of one full cycle.
Try a similar one
Find the amplitude of y = 5cos(3x) + 3.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Multiply by π/180: 45 × π/180 = 45π/180 = π/4, so the answer is 14.
✓ Correct!
Not quite. The answer is
💡 Multiply by π/180: 45 × π/180 = 45π/180 = π/4, so the answer is 14.
💡 How to solve: Radians, Arc Length & Sector Area
To change degrees to radians multiply by π/180; to change radians to degrees multiply by 180/π. With the angle θ in radians, the arc length is s = rθ and the sector area is A = (12)r2θ.
Try a similar one
Convert 360° to radians: 360° = ___π
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Subtract 360° once: 390° − 360° = 30°. The angle is 30°.
✓ Correct!
Not quite. The answer is
💡 Subtract 360° once: 390° − 360° = 30°. The angle is 30°.
💡 How to solve: Coterminal & Reference Angles (Degrees & Radians)
Coterminal angles end in the same place: add or subtract 360° (or 2π) until the angle is in the range you want, e.g. 430° - 360° = 70° and -110° + 360° = 250°. The reference angle is the acute angle between the terminal side and the x-axis: in quadrant I it is θ, in II it is 180° - θ, in III it is θ - 180°, and in IV it is 360° - θ (use π and 2π for radians). For an angle outside 0° to 360°, find its coterminal angle first.
Try a similar one
Find the angle between 0° and 360° that is coterminal with 710°.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The highest points of the graph are at y = 5 and the lowest at y = 1. The midline is halfway between them: (5 + 1) ÷ 2 = 6 ÷ 2 = 3, so the midline is y = 3.
✓ Correct!
Not quite. The answer is
💡 The highest points of the graph are at y = 5 and the lowest at y = 1. The midline is halfway between them: (5 + 1) ÷ 2 = 6 ÷ 2 = 3, so the midline is y = 3.
💡 How to solve: Amplitude, Period & Midline of Sine and Cosine
For y = a sin(bx) + d or y = a cos(bx) + d: the amplitude is |a|, the period is 2π ÷ b, and the midline is y = d. The maximum value is d + |a| and the minimum is d - |a|. On a graph, the amplitude is half the distance from a maximum to a minimum, and the period is the horizontal length of one full cycle.
Try a similar one
Find the amplitude of y = sin(4x) + 1.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Log in to save your progress.
Grade 11 Quiz: Trigonometry — Easy Version 1
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.