Get started

Algebra 2104Updated Sep 19, 20262 pages

Understanding Trigonometry: Solving Angles in Degrees and Radians

Report
user profile picture
Kaylin Sheffer@kaylinshef
Add to Google sources
Trigonometry builds on the relationship between angles and sides of triangles. Day 2 of basic trig covers the unit circle, quadrants, and solving for angles in both degrees and radians - concepts you'll need for everything from calculus to engineering.
Basic Trig / Solving in Degrees and Radians – page 1

Sign up to see the content.
It's free!

Unit Circle & Quadrants

The unit circle helps us understand trig functions across all four quadrants. In this circle with radius 1, each point (x,y)(x,y) corresponds to specific trig values. Remember that xx represents the adjacent side (cosine) and yy represents the opposite side (sine).

Each quadrant has its own sign pattern for trig functions. Sine is positive in Q1 and Q2, while cosine is positive in Q1 and Q4. Tangent is positive in Q1 and Q3. A helpful memory trick is "All Students Take Calculus" - All (Q1), Sine (Q2), Tangent (Q3), Cosine (Q4).

To find missing coordinates on the unit circle, use the Pythagorean identity: x2+y2=1x^2+y^2=1. For example, if you know a point has y=47y=\frac{4}{7}, you can find xx by solving x2+(47)2=1x^2+(\frac{4}{7})^2=1, which gives x=±337x=\pm\frac{\sqrt{33}}{7}.

💡 When solving trig problems, always identify the quadrant first! This tells you whether your final answer should be positive or negative.

Basic Trig / Solving in Degrees and Radians – page 2

Sign up to see the content.
It's free!

Radians & Solving for θ

Radians measure angles using the arc length created on a unit circle. One complete revolution equals 2π2\pi radians or 360°360°. Common angles include π6\frac{\pi}{6} (30°), π4\frac{\pi}{4} (45°), and π3\frac{\pi}{3} (60°).

When solving for an angle θ, you need to find all possible solutions within your given range. For example, if sin⁡θ=−32\sin θ = \frac{-\sqrt{3}}{2} and θ is in the range [0°,360°][0°, 360°], you must determine which quadrants have negative sine (Q3 and Q4) and find the reference angles.

Converting between degrees and radians is straightforward - multiply degrees by π180°\frac{\pi}{180°}. For example, 210°=30°×7=π6×7=7π6210° = 30° × 7 = \frac{\pi}{6} × 7 = \frac{7\pi}{6}. When dealing with large radian values like 13π413\frac{\pi}{4}, subtract multiples of 2π2\pi to find the equivalent position on the unit circle.

💡 When solving for θ with a negative trig value, always check both possible quadrants where that function is negative!

We thought you’d never ask...

Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.

You can download the app in the Google Play Store and in the Apple App Store.

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Similar Content

Pre-Calculus

Sketching sine and cosine graphs and inverse trig functions

PreCalc Trigonometric Functions

87
Pre-Calculus

precal review

This is an assignment about Pre-Calculus.

102
Algebra 2

(honors) Algebra 2 Trigonometry

Unit circle trig ranging from simple right triangle trig to modeling with sinusoids and more complex story problems

9th45333
Pre-Calculus

Reference Angle

This is an assignment about reference angles

412
Pre-Calculus

Trigonometry

SOH CAH TOA

40
Pre-Calculus

Pre-Cal Review

This is an assignment about reviewing precal

248
See more

Most popular content: Algebra 2

Algebra 2

Absolute Value Inequalities

This is a very helpful document and is a very good review.

18224
Algebra 2

Properties of Real Numbers

Notes about the topic

1412
Algebra 2

Solving Rational Equations

Different rational equations and how to accurately solve them

9th1373
Algebra 2

Arithmetic and Geometric Sequences: Recursive and Explicit Rules

Understanding the recursive and explicit rules for arithmetic and geometric sequences and how to convert between them.

10th451
Algebra 2

Set and Interval Notation

Learn how to complete a table, graph solution sets, and state domain and range using interval notation in inequality notation.

10th1122
Algebra 1

Math Function Notes

General Math Function Notes

9th29812

Most popular content

Fun Stuff

DMV Practice Test 1

First set of Questions from DMV Handbook

1,446131
Algebra

FAR NOTES- CPM

Compiled by CPM

College2,14147
Algebra

FAR NOTES - KUYA WOWOWIE

Far notes by Kuya Wowowie

College97618
Algebra

FAR NOTES-HERCULES

LAST MINUTE NOTES BY HERCULES CPA

College1,21118
Algebra

RFBT NOTES- HERCULES

LAST MINUTE NOTES BY HERCULES CPA

College93016
Algebra

AFAR NOTES- CPM

Compiled by CPM

College1,33617
Physics

Physics Reviewer

This is an extensive physics reviewer.

11th1,68336
Algebra

TAX NOTES - CPM

COMPILED BY CPM

College1,06220
AP Physics 1

Newton's Second Law of Motion

A detailed explanation of Concept of Newton's Second Law of Motion, Examples, Formulas, and Sample Problems with solution.

45214

Students love us, and so will you.

4.6/5App Store
4.7/5Google Play
Stefan SiOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Samantha KlichAndroid user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

AnnaiOS user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.