Question

Graph the given function over one period. $$y=-2 \cos (\pi x)$$

   Graph the given function over one period.
$$y=-2 \cos (\pi x)$$

Precalculus

Cynthia Young 2nd Edition

Chapter 5, Problem 28

Instant Answer

Solved by Expert Robert Leedy

06/14/2020

Step 1

The amplitude is the absolute value of the coefficient of the cosine function, which in this case is 2. The period is determined by the coefficient of x inside the cosine function. In this case, it is $\pi$. The period of the function is $\frac{2\pi}{|\pi|}$, Show more…

Show all steps

lock

Thanks for your feedback!

Graph the given function over one period. $$y=-2 \cos (\pi x)$$

Play audio

Feedback

Powered by NumerAI

Robert Leedy and 88 other subject Precalculus educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Reflection

A reflection occurs when the graph of the function is flipped over a specific axis. In the given function, the negative sign indicates a reflection over the horizontal axis, changing the orientation of the wave while preserving its shape. This concept is important for predicting and sketching the correct position of the function.

Period

The period is the length of one complete cycle of the function. For cosine functions, it is determined by the coefficient inside the argument. The period informs how frequently the function repeats itself over the x-axis, and calculating it correctly is vital for graphing one full cycle of the function accurately.

Trigonometric Function Transformations

This concept covers modifications applied to basic trigonometric functions, such as scaling, reflecting, and shifting, which alter the graph's shape, size, and orientation. In the context of cosine functions, these transformations can change the amplitude, period, and vertical position, which are essential for accurately graphing the function over a specific interval.

Amplitude

Amplitude refers to the 'height' of the wave, specifically the absolute value of the coefficient in front of the trigonometric function. It denotes the maximum displacement from the central axis and is crucial for determining the vertical stretch or compression of the graph.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later