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Graphs of Sine & Cosine — Easy Worksheet 1
Grade 12 · MathSheets 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°
✓ Correct!
Not quite. The answer is
💡 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 = 6cos(4x): 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.
✓ Correct!
Not quite. The answer is
💡 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 = sin(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.
✓ Correct!
Not quite. The answer is
💡 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 = cos(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.
✓ Correct!
Not quite. The answer is
💡 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(x): 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.
✓ Correct!
Not quite. The answer is
💡 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 = 6cos(x): What is the amplitude?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 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(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.
✓ Correct!
Not quite. The answer is
💡 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(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.
✓ Correct!
Not quite. The answer is
💡 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 = cos(x): What is the amplitude?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Graphs of Sine & Cosine — Easy Worksheet 1
Answer each question. x is measured in degrees; give periods and phase shifts in degrees and the midline as y = k.