Coterminal Angles - Varsity Tutors

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Coterminal Angles

Study Guide

Key Definition

Coterminal angles are angles in standard position that have a common terminal side. For example, $30°$, $$−330^\circ$$, and $390°$ are all coterminal.

Important Notes

  • To find a positive and a negative angle coterminal with a given angle, you can add and subtract $360°$ if the angle is measured in degrees or $2π$ if the angle is measured in radians.

Mathematical Notation

$\pi$ represents the ratio of a circle's circumference to its diameter and is approximately equal to 3.14.Remember to use proper notation when solving problems

Why It Works

Coterminal angles work because they describe the same position or rotation despite having different degree measurements.

Remember

You can always find a coterminal angle by adding or subtracting multiples of $360°$ or $2π$.

Quick Reference

Positive Coterminal Angle:$\text{angle} + 360°$Negative Coterminal Angle:$\text{angle} - 360°$Positive Coterminal Angle (radians):$\text{angle} + 2\pi$Negative Coterminal Angle (radians):$\text{angle} - 2\pi$

Understanding Coterminal Angles

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Beginner Explanation

Coterminal angles are angles that share the same terminal side. For example, the angles $30°$, $$−330^\circ$$, and $390°$ are all coterminal since they all end up at the same position.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

2

Real-World Problem

Question ExerciseIntermediate

Radial Clock Scenario

Imagine a clock where the hour hand moves in radians instead of degrees. If the hour hand is currently at $\frac{\pi}{3}$ radians, what position will it be in after it rotates by $2\pi$ radians?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Find a negative angle that's coterminal with $120°$.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Which of the following angles is NOT coterminal with $60°$?

A$420°$B$$−300^\circ$$C$780°$D$150°$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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