Trigonometric functions (DP2)

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?

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

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

Open Ended

Explain how changing the amplitude (A) and central value (C) affects the shape and position of a sine wave.

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.

Fill in the Blanks

The period of the tangent function is

.

Open Ended

How do intercepts and asymptotes influence the behavior and boundaries of trigonometric graphs?

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.

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')

Open Ended

Explain how trigonometric functions are used to model both ocean tides and seasonal temperature changes. What parameters are important in each case?

Open Ended

Describe how phase shift ('D') is important in electrical engineering, particularly in alternating current (AC) circuits.

Fill in the Blanks

GPS uses

to calculate a receiver's exact location by measuring distances and angles between the receiver and multiple satellites.

Multiple Select

Which of the following are modeled using trigonometric waves in real-world applications?

• Sound waves

• Heartbeats

• Ocean tides

• GPS triangulation

Open Ended

What questions do you still have about how trigonometry helps us understand the patterns and rhythms found in nature?

Open Ended

How do repeating cycles in nature, such as heartbeats, tides, musical notes, and pendulums, demonstrate the concept of a mathematical blueprint?