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  2. AP Pre Calculus
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Sinusoidal Functions

Henry Lee

Henry Lee

5 min read

Next Topic - Sinusoidal Function Transformations
Study Guide Overview

This study guide covers sinusoidal functions, including sine and cosine. It defines sinusoidal functions and explains their key characteristics: period, frequency, midline, amplitude, symmetry (odd and even), oscillation, and concavity. It also emphasizes the relationship between period and frequency and provides tips for identifying the midline.

#Sinusoidal Functions: Your Ultimate Review 🚀

Hey there, future AP Pre-Calculus master! Let's dive into the world of sinusoidal functions. Think of this as your pre-exam power-up – everything you need, nothing you don't. Let's get started!

#Understanding Sinusoidal Functions

#What are Sinusoidal Functions?

  • A sinusoidal function is any function that looks like a sine or cosine curve – oscillating and periodic. Both sine and cosine functions are sinusoidal, and so are their transformations.

  • Key Idea: The cosine function is just a transformed sine function:

    cos(θ)=sin(θ+π2)cos(θ) = sin(θ + \frac{π}{2})cos(θ)=sin(θ+2π​)

    This means the cosine curve is the sine curve shifted to the left by π2\frac{π}{2}2π​ units. Think of it as a horizontal slide! ➡️

    ![](https://zupay.blob.core.windows.net/resources/files/0baca4f69800419293b4c75aa2870acd_6b0ad7_419.pn...

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Previous Topic - Sine and Cosine Function GraphsNext Topic - Sinusoidal Function Transformations

Question 1 of 10

🎉 What type of function is described as oscillating and periodic, resembling a sine or cosine curve?

Linear Function

Quadratic Function

Sinusoidal Function

Exponential Function