# Trigonometry Calculator

Trigonometry Calculator computes the value of a trigonometric ratio at a certain angle. Trigonometry deals with the study of the relationship between the side lengths and angles of a right triangle.The word trigonometry is formed by clubbing words 'Trigonon' and 'Metron' which means triangle and measure respectively.

## What is a Trigonometry Calculator?

Trigonometry Calculator is an online tool that helps to calculate the value of the various trigonometric ratios for a given angle. Sine, cosine, tangent, cotangent, secant, and cosecant are the six trigonometric ratios. To use the **trigonometry calculator**, enter the value in the input box and select the trigonometric ratio from the drop-down list.

### Trigonometry Calculator

## How to Use the Trigonometry Calculator?

Please follow the steps below to find the value of the trigonometric ratio for a given angle using the online trigonometry calculator:

**Step 1:**Go to Cuemath's online trigonometry calculator.**Step 2:**Enter the angle (in degrees) in the given input box and choose the trigonometric ratio from the drop-down list.**Step 3:**Click on the**"Calculate"**button to find the value of the trigonometric ratio for the given angle.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Trigonometry Calculator Work?

In a right-angled triangle, one angle measures 90 degrees while the other two are acute angles. Furthermore, the three sides of a right triangle can be categorized as follows:

**Perpendicular**- The side opposite to the angle θ.**Base**- The side adjacent to the angle θ.**Hypotenuse**- This is the longest side of the triangle. It is the side opposite to the right angle.

To establish a relationship between the angles and the ratio of the sides in a right triangle we use trigonometric ratios. These are given as follows:

- sin θ (sine) = Perpendicular / Hypotenuse
- cos θ (cosine) = Base / Hypotenuse
- tan θ (tangent) = Perpendicular / Base

The remaining three ratios are reciprocals of the above-mentioned trigonometric ratios. These are given by:

- cosec θ (cosecant) = 1/sin θ = Hypotenuse / Perpendicular
- sec θ (secant) = 1/cos θ = Hypotenuse / Base
- cot θ (cotangent) = 1/tan θ = Base / Perpendicular

The trigonometric ratios for some standard angle values can be observed from the trigonometry table given below:

## Solved Examples on Trigonometry Calculator

**Example 1:**

Find the value of cos (30^{0}) and verify it using the online trigonometry calculator.

**Solution:**

The derived standard value of cos (30^{0}) is √3/2.

Therefore, cos (30^{0}) = 0.866

**Example 2:**

Find the value of sin (-45^{0}) and verify it using the online trigonometry calculator.

**Solution:**

sin (-45^{0}) = -sin (45^{0})

The derived standard value of sin (45^{0}) is 1/√2.

Therefore, sin (-45^{0}) = -1/√2 = -0.7071.

Similarly, you can try the trigonometry calculator to find the values of the trigonometric ratios for the following:

- θ = -60°
- θ = 180°

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