Master Trigonometry

From basic angles to advanced applications. Learn visually, practice interactively, and master trigonometry at your own pace.

12+ Lessons
50+ Practice Problems
100% Interactive

The Unit Circle

Drag the point around the circle to see how sine, cosine, and tangent values change in real-time.

degrees
sin(θ) y-coordinate
0.707
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$
cos(θ) x-coordinate
0.707
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
tan(θ) slope
1.000
$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$
Point: (0.707, 0.707) Radians: π/4

Learn Step by Step

Progress from fundamentals to advanced topics with our structured curriculum.

01

Understanding Angles

Learn about degrees, radians, and how to convert between them.

15 min Beginner
02

Right Triangle Basics

Discover the relationship between sides and angles in right triangles.

20 min Beginner
03

SOH CAH TOA

Master the fundamental ratios: sine, cosine, and tangent.

25 min Beginner
04

Introduction to Unit Circle

Understand how the unit circle connects angles to trig functions.

30 min Beginner

Graph Explorer

Adjust parameters to see how they affect the shape of trigonometric functions.

y = sin(x)

Test Your Knowledge

Challenge yourself with interactive quizzes and get instant feedback.

Question 1 of 10
Score: 0
Beginner

What is sin(30°)?

Practice Problems

Problem 1 Beginner

A ladder 10 meters long leans against a wall at an angle of 60° from the ground. How high up the wall does the ladder reach?

Problem 2 Intermediate

Simplify: sin²(x) + cos²(x) + tan²(x)

Problem 3 Advanced

Find all solutions to 2sin²(x) - sin(x) - 1 = 0 in the interval [0, 2π).

Essential Identities

Keep these fundamental relationships at your fingertips.

Pythagorean Identities

$\sin^2(\theta) + \cos^2(\theta) = 1$
$1 + \tan^2(\theta) = \sec^2(\theta)$
$1 + \cot^2(\theta) = \csc^2(\theta)$

Reciprocal Identities

$\csc(\theta) = \frac{1}{\sin(\theta)}$
$\sec(\theta) = \frac{1}{\cos(\theta)}$
$\cot(\theta) = \frac{1}{\tan(\theta)}$

Double Angle Formulas

$\sin(2\theta) = 2\sin(\theta)\cos(\theta)$
$\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)$
$\tan(2\theta) = \frac{2\tan(\theta)}{1-\tan^2(\theta)}$

Sum & Difference

$\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B$
$\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B$

Special Angles

θ 30° 45° 60° 90°
sin 0 ½ √2/2 √3/2 1
cos 1 √3/2 √2/2 ½ 0
tan 0 √3/3 1 √3

Co-function Identities

$\sin(\frac{\pi}{2} - \theta) = \cos(\theta)$
$\cos(\frac{\pi}{2} - \theta) = \sin(\theta)$
$\tan(\frac{\pi}{2} - \theta) = \cot(\theta)$

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