# Trigonometric Ratios

Trigonometry is the branch of mathematics concerned with the sides and angles of a right-angled triangle. As a result, trigonometric ratios are evaluated in terms of sides and angles.

The trigonometric ratios of a right-angled triangle’s sides with regard to any of its acute angles are known as that angle’s trigonometric ratios. There are three sides in a right-angled triangle that are considered for deriving a trigonometric ratio. They are as follows:

1) Opposite side: It is the side opposite to the angle taken for a reference.
2) Adjacent side: It is the side adjacent to the angle taken for a reference.
3) Hypotenuse: It is the longest side in the triangle that is opposite to the right angle.

## How to obtain the trigonometric ratios?

The six trigonometric ratios in a right-angled triangle are sine, cosine, tangent, secant, cosecant, and cotangent. These can be obtained as shown below. Consider ΔPQR with Q to be a right angle. Refer to the image below. • Sine: Sine of an angle is the ratio of the opposite side to the hypotenuse.
• Cosine: Cosine of an angle is the ratio of the adjacent side to the hypotenuse.
• Tangent: Tangent of an angle is the ratio of the opposite side to the adjacent side.
• Cosecant: Cosecant of an angle is the ratio of the hypotenuse to the opposite side. It is the inverse of the sine.
• Secant: Secant of an angle is the ratio of the hypotenuse to the adjacent side. It is the inverse of the cosine.
• Cotangent: Cotangent of an angle is the ratio of the adjacent side to the opposite side.
• The trigonometric ratios are interlinked with each other. Each ratio is written in terms of other ratio. The values of the trigonometric ratios for some standard angles are given in the image below. Example 1: Find the trigonometric ratios for the given triangle below. Solution: Trigonometric ratios can be determined for angles A and C. First, let us see on how to write trigonometric ratios for angle A. In the similar way, the trigonometric ratios for angle C are written as follows: Example 2: If and then find the values of tanθ and cotθ.

Know more about other concepts of Trigonometry on What is Trigonometry – An Introduction and Trigonometric Identities

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