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Questions and Answers
What is the period of the function y = 3 sin(x)?
What is the period of the function y = 3 sin(x)?
2π
What is the amplitude of the function y = 3 sin(x)?
What is the amplitude of the function y = 3 sin(x)?
3
What is the phase shift of the function y = 3 sin(x)?
What is the phase shift of the function y = 3 sin(x)?
0
What is the vertical shift of the function y = 3 sin(x)?
What is the vertical shift of the function y = 3 sin(x)?
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What is the period of the function y = -2cos(x)?
What is the period of the function y = -2cos(x)?
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What is the period of the function y = cos(x - π/2)?
What is the period of the function y = cos(x - π/2)?
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What is the amplitude of the function y = cos(x - π/2)?
What is the amplitude of the function y = cos(x - π/2)?
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What is the phase shift of the function y = cos(x - π/2)?
What is the phase shift of the function y = cos(x - π/2)?
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What is the vertical shift of the function y = cos(x - π/2)?
What is the vertical shift of the function y = cos(x - π/2)?
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What is the period of the function y = -sin(x + π/3)?
What is the period of the function y = -sin(x + π/3)?
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What is the amplitude of the function y = -sin(x + π/3)?
What is the amplitude of the function y = -sin(x + π/3)?
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What is the phase shift of the function y = -sin(x + π/3)?
What is the phase shift of the function y = -sin(x + π/3)?
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What is the vertical shift of the function y = -sin(x + π/3)?
What is the vertical shift of the function y = -sin(x + π/3)?
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What is the period of the function y = (1/3)cos(x/2 + π/3)?
What is the period of the function y = (1/3)cos(x/2 + π/3)?
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What is the amplitude of the function y = (1/3)cos(x/2 + π/3)?
What is the amplitude of the function y = (1/3)cos(x/2 + π/3)?
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What is the phase shift of the function y = (1/3)cos(x/2 + π/3)
What is the phase shift of the function y = (1/3)cos(x/2 + π/3)
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What is the vertical shift of the function y = (1/3)cos(x/2 + π/3)?
What is the vertical shift of the function y = (1/3)cos(x/2 + π/3)?
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What is the period of the function y = cos(3x - 2π) + 4?
What is the period of the function y = cos(3x - 2π) + 4?
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What is the amplitude of the function y = cos(3x - 2π) + 4?
What is the amplitude of the function y = cos(3x - 2π) + 4?
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What is the phase shift of the function y = cos(3x - 2π) + 4?
What is the phase shift of the function y = cos(3x - 2π) + 4?
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What is the vertical shift of the function y = cos(3x - 2π) + 4?
What is the vertical shift of the function y = cos(3x - 2π) + 4?
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What is the period of the function y = 2tan(x/4) - 3?
What is the period of the function y = 2tan(x/4) - 3?
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What is the period of the function y = (1/3)tan(-2x - π) + 1 ?
What is the period of the function y = (1/3)tan(-2x - π) + 1 ?
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What is the period of the function y = csc(x - π/4) - 2?
What is the period of the function y = csc(x - π/4) - 2?
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What is the period of the function y = (1/3)cot(2x + 3π/2) + 1?
What is the period of the function y = (1/3)cot(2x + 3π/2) + 1?
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Study Notes
Graphing Trigonometric Functions
- Worksheet 15 Key provides examples of graphing trigonometric functions with different transformations.
- Each example demonstrates a specific trigonometric function (sine, cosine, tangent, secant, cosecant, cotangent) with variations in amplitude, period, phase shift, and vertical shift.
- The transformations affect the graph's shape and position.
Function Examples
-
y = 3sin(x):
- Period: 2π
- Amplitude: 3
- Phase Shift: 0
- Vertical Shift: 0
-
y = sin(3x):
- Period: 2π/3
- Amplitude: 1
- Phase Shift: 0
- Vertical Shift: 0
-
y = -2cos(x):
- Period: 2π
- Amplitude: 2
- Phase Shift: 0
- Vertical Shift: 0
-
y = cos(x - π/2):
- Period: 2π
- Amplitude: 1
- Phase Shift: π/2
- Vertical Shift: 0
-
y = -sin(x) + (x + π/3):
- Period: 2π
- Amplitude: 1
- Phase Shift: -π/3
- Vertical Shift: 0
-
y = sin(2x - π):
- Period: π
- Amplitude: 1
- Phase Shift: π/2
- Vertical Shift: 0
-
y = cos(x/3):
- Period: 8π
- Amplitude: 1
- Phase Shift: 0
- Vertical Shift: 0
-
y = cos(3x − 2π) + 4:
- Period: 2π/3
- Amplitude: 1
- Phase Shift: 2π/3
- Vertical Shift: 4
-
y = sin(x + 1) - 2 -Amplitude =1 -Period =2π -Phase Shift = -1
- Vertical Shift=-2
-
Additional examples include variations of tangent, cotangent, secant, and cosecant functions with similar transformations.
Graphing Strategy
- Graphing strategies mention showing several cycles to illustrate phase shifts; finding parameters like period and amplitude by referring to the base function.
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Description
This quiz focuses on the graphing of trigonometric functions, specifically through Worksheet 15 Key. Each example illustrates how various transformations, such as amplitude, period, and phase shift, impact the shape and position of sine, cosine, tangent, and other functions. Test your understanding of these concepts with detailed function examples.
