Master

Cosine Function

Master cosine function with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Cosine Function

Study Guide

Key Definition

The cosine function is a periodic function which is very important in trigonometry. For a given angle measure $\theta$, the x-coordinate of the point where the other side of the angle intersects the unit circle is $\cos(\theta)$.

Important Notes

The cosine function is positive in quadrants I and IV and negative in quadrants II and III.
The range of the cosine function is -1 ≤ y ≤ 1.
The cosine function is periodic with a period of 2$\pi$.

Mathematical Notation

$\cos(\theta)$ represents the cosine of angle $\theta$.

Remember to use proper notation when solving problems

Why It Works

The cosine function works by projecting the angle onto the x-axis of the unit circle.

Remember

Remember the values of cosine at 0, $\frac{\pi}{2}$, $\pi$, and $\frac{3\pi}{2}$.

Quick Reference

Cosine of 0:$\cos(0) = 1$

Cosine of $\frac{\pi}{2}$:$\cos(\frac{\pi}{2}) = 0$

Cosine of $\pi$:$\cos(\pi) = -1$

Cosine of $\frac{3\pi}{2}$:$\cos(\frac{3\pi}{2}) = 0$

Understanding Cosine Function

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The cosine function is a way of relating angles and lengths in a unit circle.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the value of $\cos(0)$?

Real-World Problem

Question Exercise

Intermediate

Football Kick Scenario

A football player kicks a ball at an angle of $\frac{\pi}{3}$ with the ground. What is the x-component of the kick's direction (assuming the positive x-axis is along the ground)?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

What is the period of the cosine function?

Challenge Quiz

Single Choice Quiz

Advanced

What is the value of $\cos(\frac{3\pi}{2})$?

Recap

Watch & Learn

Review key concepts and takeaways