Trigonometric Functions Calculator

Compute all 6 trig functions at once for any angle. Shows sin, cos, tan, csc, sec, cot with quadrant info.

Enter Angle

Q I (0-90)All positive
Q II (90-180)sin, csc positive
Q III (180-270)tan, cot positive
Q IV (270-360)cos, sec positive

All Trigonometric Functions

Angle
45°
Quadrant I
FunctionValueInverse

Angle Conversions

All Six Trigonometric Functions

The six trigonometric functions are the fundamental building blocks of trigonometry. Given an angle, each function returns a specific ratio related to a right triangle or the unit circle. This calculator evaluates all six at once, saving time and providing a complete picture.

Function Definitions

sin and csc

Sine is the y-coordinate on the unit circle. Cosecant is its reciprocal.

sin(x) = opp/hyp, csc(x) = 1/sin(x)

cos and sec

Cosine is the x-coordinate on the unit circle. Secant is its reciprocal.

cos(x) = adj/hyp, sec(x) = 1/cos(x)

tan and cot

Tangent is sine/cosine. Cotangent is its reciprocal.

tan(x) = sin/cos, cot(x) = cos/sin

Quadrant Sign Rules (ASTC)

The mnemonic "All Students Take Calculus" helps remember which functions are positive in each quadrant: All in Q I, Sine in Q II, Tangent in Q III, Cosine in Q IV. The reciprocal functions follow the same sign as their primary counterpart.

Reference Angles

A reference angle is the acute angle formed between the terminal side and the x-axis. It is always between 0 and 90 degrees and helps determine the absolute value of trig functions in any quadrant.