Trigonometry Calculator

Trigonometric Values

About Trigonometry Calculator

Trigonometry Fundamentals

Trigonometry studies relationships between angles and sides of triangles. The six trigonometric functions (sin, cos, tan, csc, sec, cot) relate the angles of a right triangle to the ratios of its sides. SOH-CAH-TOA helps remember: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. These functions extend beyond triangles to model periodic phenomena: sound waves, light, tides, seasonal patterns, and circular motion.

Key Trigonometric Values

Special angles have exact values: sin(30)=1/2, sin(45)=sqrt(2)/2, sin(60)=sqrt(3)/2. cos(30)=sqrt(3)/2, cos(45)=sqrt(2)/2, cos(60)=1/2. tan(45)=1, tan(30)=1/sqrt(3), tan(60)=sqrt(3). Key identities: sin^2 + cos^2 = 1, tan = sin/cos, sin(2x) = 2sin(x)cos(x).

How to Use This Calculator

Enter an angle to compute all six trig functions, or enter a function value to find the angle (inverse trig). Toggle between degrees and radians. The calculator shows exact values for special angles, verifies identities, and can solve right triangles given two pieces of information.

Frequently Asked Questions

What is the difference between degrees and radians?

Degrees divide a full circle into 360 parts. Radians measure the angle by arc length: a full circle = 2*pi radians. To convert: radians = degrees x pi/180. Radians are preferred in calculus and physics.

What does SOH-CAH-TOA mean?

A mnemonic for right triangles: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. It helps remember which sides correspond to which function.

When is tangent undefined?

Tangent = sin/cos, so it is undefined when cos = 0. This occurs at 90 degrees (pi/2) and 270 degrees (3*pi/2) and their coterminal angles. Graphically, these are vertical asymptotes.