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Calculator Answers

Sin Cos Tan Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A sin cos tan calculator evaluates the primary trigonometric functions (sine, cosine, and tangent) and their reciprocal functions (cosecant, secant, and cotangent) for a given angle. The user can toggle between degrees and radians. The calculator handles edge cases where functions like tangent or secant are undefined (e.g., at 90 degrees or pi/2 radians) by displaying 'undefined' rather than crashing.

Calculate standard and reciprocal trigonometric values for any angle in degrees or radians.

See also: Law of Sines Calculator, Law of Cosines Calculator, and Right Triangle Calculator.

Quick Answer

Find the sine, cosine, and tangent of an angle in degrees or radians. Computes all standard and reciprocal trigonometric functions.

Enter any positive or negative angle. · e.g. 45

Angle unit

Trigonometric Values

Primary Results for 45°

sin = 0.7071

cos = 0.7071 · tan = 1

sine: sin(θ)0.7071
cosine: cos(θ)0.7071
tangent: tan(θ) = sin/cos1
cosecant: csc(θ) = 1/sin1.4142
secant: sec(θ) = 1/cos1.4142
cotangent: cot(θ) = cos/sin1
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Examples

30 Degrees

30° — sin = 0.5000 · cos = 0.8660 · tan = 0.5774

pi/2 Radians (90°)

1.5708 rad (π/2) — sin = 1.0000 · cos = 0 · tan = Undefined

How it works

Unit Circle Definitions

Trigonometric functions can be defined using coordinates on a unit circle (a circle with radius 1 centered at the origin):

  • sin(θ) = y-coordinate
  • cos(θ) = x-coordinate
  • tan(θ) = y / x

Reciprocal Ratios

  • csc(θ) = 1 / sin(θ)
  • sec(θ) = 1 / cos(θ)
  • cot(θ) = 1 / tan(θ)

Disclaimer

For educational purposes. Verify results for critical applications.

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Frequently asked questions

The primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan). They relate the angles of a right triangle to the ratios of its sides.

Reciprocal functions are defined as 1 divided by a primary function: Cosecant (csc = 1/sin), Secant (sec = 1/cos), and Cotangent (cot = 1/tan).

Tangent is defined as sine divided by cosine. At 90 degrees, cosine is equal to 0, which means tangent requires dividing by 0. Because division by zero is mathematically undefined, tangent at 90° (and 270°, etc.) is undefined.

To convert degrees to radians, multiply the angle in degrees by pi and divide by 180. Formula: radians = degrees × (π / 180).