Or press and hold the picture and choose “Save image”.
for Whoobee's shop
Graphs of Sine & Cosine — Easy Worksheet 2
Grade 12 · Whoobee Name: ____________________ Date: __________
Answer each question. x is measured in degrees; give periods and phase shifts in degrees and the midline as y = k.
How to solve
For y = A sin(B(x - C)) + D (or cos): the amplitude is |A|, the period is 360°/B, the midline is y = D, the maximum is D + |A|, and the phase shift is C (right if C > 0, left if C < 0). On a graph, the amplitude is half the distance from a peak to a trough.
Example
For y = sin(2x): What is the period, in degrees?
Answer: 180°
Not quite. The answer is
💡 The amplitude is |A|, the size of the number in front of sin. Here A = 1, so the amplitude is |1| = 1.
✓ Correct!
Not quite. The answer is
💡 The amplitude is |A|, the size of the number in front of sin. Here A = 1, so the amplitude is |1| = 1.
💡 How to solve: Graphs of Sine & Cosine
For y = A sin(B(x - C)) + D (or cos): the amplitude is |A|, the period is 360°/B, the midline is y = D, the maximum is D + |A|, and the phase shift is C (right if C > 0, left if C < 0). On a graph, the amplitude is half the distance from a peak to a trough.
Try a similar one
For y = 6sin(3x): What is the amplitude?
✓ 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 curve makes exactly one full cycle from 0° to 360°, so the period is 360°.
✓ Correct!
Not quite. The answer is
💡 The curve makes exactly one full cycle from 0° to 360°, so the period is 360°.
💡 How to solve: Graphs of Sine & Cosine
For y = A sin(B(x - C)) + D (or cos): the amplitude is |A|, the period is 360°/B, the midline is y = D, the maximum is D + |A|, and the phase shift is C (right if C > 0, left if C < 0). On a graph, the amplitude is half the distance from a peak to a trough.
Try a similar one
For y = 5cos(2x): What is the period, in degrees?
✓ 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
💡 Here B = 4, the number multiplying x, so the period is 360° ÷ B = 360° ÷ 4 = 90°.
✓ Correct!
Not quite. The answer is
💡 Here B = 4, the number multiplying x, so the period is 360° ÷ B = 360° ÷ 4 = 90°.
💡 How to solve: Graphs of Sine & Cosine
For y = A sin(B(x - C)) + D (or cos): the amplitude is |A|, the period is 360°/B, the midline is y = D, the maximum is D + |A|, and the phase shift is C (right if C > 0, left if C < 0). On a graph, the amplitude is half the distance from a peak to a trough.
Try a similar one
For y = 3sin(2x): What is the amplitude?
✓ 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 curve repeats 2 times from 0° to 360°, so one cycle takes 360° ÷ 2 = 180°.
✓ Correct!
Not quite. The answer is
💡 The curve repeats 2 times from 0° to 360°, so one cycle takes 360° ÷ 2 = 180°.
💡 How to solve: Graphs of Sine & Cosine
For y = A sin(B(x - C)) + D (or cos): the amplitude is |A|, the period is 360°/B, the midline is y = D, the maximum is D + |A|, and the phase shift is C (right if C > 0, left if C < 0). On a graph, the amplitude is half the distance from a peak to a trough.
Try a similar one
For y = 3sin(2x): What is the amplitude?
✓ 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
💡 Here B = 1, the number multiplying x, so the period is 360° ÷ B = 360° ÷ 1 = 360°.
✓ Correct!
Not quite. The answer is
💡 Here B = 1, the number multiplying x, so the period is 360° ÷ B = 360° ÷ 1 = 360°.
💡 How to solve: Graphs of Sine & Cosine
For y = A sin(B(x - C)) + D (or cos): the amplitude is |A|, the period is 360°/B, the midline is y = D, the maximum is D + |A|, and the phase shift is C (right if C > 0, left if C < 0). On a graph, the amplitude is half the distance from a peak to a trough.
Try a similar one
For y = 3cos(2x): What is the amplitude?
✓ 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 curve makes exactly one full cycle from 0° to 360°, so the period is 360°.
✓ Correct!
Not quite. The answer is
💡 The curve makes exactly one full cycle from 0° to 360°, so the period is 360°.
💡 How to solve: Graphs of Sine & Cosine
For y = A sin(B(x - C)) + D (or cos): the amplitude is |A|, the period is 360°/B, the midline is y = D, the maximum is D + |A|, and the phase shift is C (right if C > 0, left if C < 0). On a graph, the amplitude is half the distance from a peak to a trough.
Try a similar one
For y = 4cos(4x): What is the amplitude?
✓ 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 amplitude is |A|, the size of the number in front of sin. Here A = 2, so the amplitude is |2| = 2.
✓ Correct!
Not quite. The answer is
💡 The amplitude is |A|, the size of the number in front of sin. Here A = 2, so the amplitude is |2| = 2.
💡 How to solve: Graphs of Sine & Cosine
For y = A sin(B(x - C)) + D (or cos): the amplitude is |A|, the period is 360°/B, the midline is y = D, the maximum is D + |A|, and the phase shift is C (right if C > 0, left if C < 0). On a graph, the amplitude is half the distance from a peak to a trough.
Try a similar one
For y = 4sin(4x): What is the amplitude?
✓ 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 curve makes exactly one full cycle from 0° to 360°, so the period is 360°.
✓ Correct!
Not quite. The answer is
💡 The curve makes exactly one full cycle from 0° to 360°, so the period is 360°.
💡 How to solve: Graphs of Sine & Cosine
For y = A sin(B(x - C)) + D (or cos): the amplitude is |A|, the period is 360°/B, the midline is y = D, the maximum is D + |A|, and the phase shift is C (right if C > 0, left if C < 0). On a graph, the amplitude is half the distance from a peak to a trough.
Try a similar one
For y = 2sin(3x): What is the amplitude?
✓ 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.
Graphs of Sine & Cosine — Easy Worksheet 2
Answer each question. x is measured in degrees; give periods and phase shifts in degrees and the midline as y = k.