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 (30⁰) and verify it using the online trigonometry calculator.

Solution:

The derived standard value of cos (30⁰) is √3/2.

Therefore, cos (30⁰) = 0.866

Example 2:

Find the value of sin (-45⁰) and verify it using the online trigonometry calculator.

Solution:

sin (-45⁰) = -sin (45⁰)

The derived standard value of sin (45⁰) is 1/√2.

Therefore, sin (-45⁰) = -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°

☛ Related Articles:

• Trigonometric Ratios
• Trigonometric Functions

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