Omni Calculator logo

Trig Function Calculator

Created by Luis Hoyos
Reviewed by Davide Borchia
Last updated: Jan 18, 2024


This trig function calculator prints the value of the six trig functions given the angle in degrees or radians. In the article below, we explain:

  • What are the 6 trig functions; and
  • How to calculate those trig functions.

In the FAQ section, we present the value of the trig functions for some of the most common angles: the values of the six trig functions for 45 degrees and 270 degrees.

The 6 trig functions.

Sine, cosine, and tangent

Sine, cosine, and tangent are the trigonometric functions of an angle. The most common way to define them is by using a right triangle and one of its angles (the angle of interest).

First, let's remember the names of the three sides of a right triangle:

Right triangle. Opposite, adjacent and hypotenuse
  • Hypotenuse: The longest side, always opposite to the right angle;
  • Opposite side: The side opposite to the angle of interest (α); and
  • Adjacent side: The side of the triangle that is neither the hypotenuse nor the opposite side.

As you can note, the hypotenuse and adjacent side form the reference angle (α).

Then, the trigonometric functions are defined as:

sin(α) = opposite/hypotenuse

cos(α) = adjacent/hypotenuse

tan(α) = opposite/adjacent

right triangle. Sine, cosine and tangent of the angle

🙋 In summary, we use the right triangle to easily define the reference angle and calculate the trigonometric functions based on the lengths of the sides.

Cosecant, secant, and cotangent

Cosecant (csc), secant (sec), and cotangent (cot) are simply the reciprocals of the three previous functions:

  • csc(α) = 1/sin(α) = hypotenuse/opposite

  • sec(α) = 1/cos(α) = hypotenuse/adjacent

  • cot(α) = 1/tan(α) = adjacent/opposite

Other trig functions calculators.

To learn more about this topic, you can visit our trigonometric functions calculator article and the following tools:

FAQ

What are the values of the six trig functions for 45 degrees?

The values of the six trig functions for 45 degrees are:

  • sin(45°) = √2/2 ≈ 0.70710678
  • cos(45°) = √2/2 ≈ 0.70710678 (the same as sin(45°))
  • tan(45°) = 1
  • sec(45°) = √2 ≈ 1.41421356
  • csc(45°) = √2 ≈ 1.41421356 (the same as sec(45°))
  • cot(45°) = 1

What are the values of the 6 trig functions for 270 degrees?

The values of the 6 trig functions for 270 degrees are:

  • sin(270°) = -1
  • cos(270°) = 0
  • tan(270°) = undefined
  • sec(270°) = 0
  • csc(270°) = undefined
  • cot(270°) = -1
Luis Hoyos
Related calculators
Angle
deg
Check out 21 similar trigonometry calculators 📐
ArccosArcsinArctan… 18 more
People also viewed…

Common multiple

Find the common multiple of a given set of numbers using common multiple calculator.

Floor function

With the floor function calculator you can discover how this function works and why it is useful.

Pizza size

Make the best pizza choice with our Pizza Size Calculator – compare sizes and prices for the perfect order!

Social Media Time Alternatives

Check what you could have accomplished if you get out of your social media bubble.
Copyright by Omni Calculator sp. z o.o.
Privacy, Cookies & Terms of Service