Trigonometric Ratios: The Key To Solving Right Triangle Problems

trigonometric ratio

a ratio of two sides of a right triangle

Trigonometric ratios are relationships between the angles and sides of a right triangle. There are six trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).

Sine (sin) – In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is expressed as sin(theta) = opposite/hypotenuse.

Cosine (cos) – In a right triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It is expressed as cos(theta) = adjacent/hypotenuse.

Tangent (tan) – In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. It is expressed as tan(theta) = opposite/adjacent.

Cosecant (csc) – In a right triangle, the cosecant of an angle is defined as the reciprocal of the sine of the angle. It is expressed as csc(theta) = hypotenuse/opposite.

Secant (sec) – In a right triangle, the secant of an angle is defined as the reciprocal of the cosine of the angle. It is expressed as sec(theta) = hypotenuse/adjacent.

Cotangent (cot) – In a right triangle, the cotangent of an angle is defined as the reciprocal of the tangent of the angle. It is expressed as cot(theta) = adjacent/opposite.

Trigonometric ratios are commonly used in trigonometry to solve problems related to angles and sides of a right triangle. It is also used in various fields such as engineering, physics, and astronomy.

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