Trigonometric functions (DP2)
Presentation
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Mathematics
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12th Grade
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Practice Problem
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Medium
Paulino Mbebe
Used 1+ times
FREE Resource
13 Slides • 15 Questions
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Open Ended
How do you think mathematical patterns, such as those seen in rhythms and cycles, influence the way we experience the world around us?
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Multiple Choice
Which of the following is an example of a repeating cycle found in nature that follows a mathematical blueprint?
Heartbeat
Random lightning strike
Sudden earthquake
Unpredictable gust of wind
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Multiple Choice
Which parameter in the equations f(x) = A sin[B(x – D)] + C and f(x) = A cos[B(x – D)] + C controls the vertical shift of the wave?
A: Amplitude
B: Period
C: Central Value
D: Phase Shift
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Open Ended
Explain how changing the amplitude (A) and central value (C) affects the shape and position of a sine wave.
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Multiple Select
Select all statements that correctly describe the effect of changing the period modifier (B) and phase shift (D) in a trigonometric wave.
Increasing B compresses the wave horizontally, making cycles shorter.
Decreasing B stretches the wave horizontally, making cycles longer.
Increasing D shifts the wave to the right.
Decreasing D shifts the wave to the left.
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Fill in the Blanks
Type answer...
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Open Ended
How do intercepts and asymptotes influence the behavior and boundaries of trigonometric graphs?
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Multiple Choice
Which of the following statements is true about the reflection of trigonometric functions across the x-axis and y-axis?
Reflection across the x-axis flips the graph vertically.
Reflection across the y-axis flips the graph horizontally.
Cosine is an even function and remains unchanged under y-axis reflection.
Sine is an odd function and changes sign under y-axis reflection.
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Multiple Choice
Which parameter of a trigonometric wave determines the volume of a sound and the strength of a heartbeat pulse?
Amplitude ('A')
Period ('B')
Central Value ('C')
Phase Shift ('D')
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Open Ended
Explain how trigonometric functions are used to model both ocean tides and seasonal temperature changes. What parameters are important in each case?
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Open Ended
Describe how phase shift ('D') is important in electrical engineering, particularly in alternating current (AC) circuits.
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Fill in the Blanks
Type answer...
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Multiple Select
Which of the following are modeled using trigonometric waves in real-world applications?
Sound waves
Heartbeats
Ocean tides
GPS triangulation
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Open Ended
What questions do you still have about how trigonometry helps us understand the patterns and rhythms found in nature?
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Open Ended
How do repeating cycles in nature, such as heartbeats, tides, musical notes, and pendulums, demonstrate the concept of a mathematical blueprint?
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