Trigonometrical Ratios

The ratio between the lengths of a pair of two sides of a right angled triangle is called a trigonometric ratio.

The three sides of a right-angled triangle give six trigonometric ratios; namely sine, cosine, tangent, cotangent, secant and cosecant. In short, these ratios are written as sin, cos, tan , cot, sec and cosec respectively.

In a right angled-triangle with acute angle A, the trigonometric ratios are defined as:

sin A = perpendicular / hypotenuse

cos A = base/ hypotenuse

tan A = perpendicular/ base

cosec A = hypotenuse/ perpendicular

sec A = hypotenuse/ base

cot A = base/perpendicular

The ratios cosec A, sec A and cot A are the reciprocal of the ratios sin A, cos A and tan A respectively.

The trigonometric ratios sin A, cos A, tan A, cot A, sec A, and cosec A are also known as trigonometric functions of A.

sin 0° = 0, cos 0° = 1, tan 0°= 0

sin 90° = 1, cos 90° = 0, tan 90°= not defined

A trigonometric equation is an equation that has one or more trigonometric ratios or trigonometric functions of an unknown angle. Solving a trigonometric equation involves steps to find the value of an unknown angle that satisfies the given equation.

Keywords: Trigonometric Ratios of Specific Angles

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