Trigonometric Functions - Examples & Applications

Interactive Simulators

Interactive ASTC Visualizer

Explore how the signs of trigonometric functions change across the four quadrants.

Hover or tap on a quadrant to see which functions are positive.

SQuadrant II

AQuadrant I

TQuadrant III

CQuadrant IV

Select a quadrant to view its properties.

Interactive Unit Circle

Drag the slider to visualize how the sine, cosine, and tangent values change as the angle rotates.

Angle ($\theta$)45°

0°360°

sin(45°)0.7071

cos(45°)0.7071

tan(45°)1.0000

Interactive Graph Explorer

Explore how parameters

A

B

C

, and

D

affect the shape of trigonometric graphs.

y = 1sin(1(x - 0)) + 0

Amplitude (A)1

Period Factor (B)1

Phase Shift (C)0

Vertical Shift (D)0

Period: 2π / |B|

Solved Problems

Problem 1: In a right triangle with legs 3 and 4, find the six trigonometric functions of angle

\theta

opposite the side of length 3.

0 of 2 Steps Completed

Problem 2: Find the exact value of

\sec(240^\circ)

0 of 4 Steps Completed

Problem 3: Determine the amplitude, period, and phase shift of

y = 3\sin(2x - \pi)

0 of 4 Steps Completed

Problem 4: The terminal side of angle

\theta

passes through the point

(-5, 12)

. Find

\sin \theta

\cos \theta

, and

\tan \theta

0 of 2 Steps Completed