Trigonometric Ratios Definition

Trigonometry has 6 basic trigonometric ratios also called trigonometric functions, they are sine, cosine, tangent, cosecant, secant, and cotangent. Now let’s look into the trigonometric functions. The six trigonometric functions are as follows,

• sine: the ratio of perpendicular and hypotenuse is defined as sine and It is represented as sin θ
• cosine: the ratio of base and hypotenuse is defined as cosine and it is represented as cos θ
• tangent: the ratio of sine and cosine of an angle is defined as a tangent. Thus the definition of tangent comes out to be the ratio of perpendicular and base and is represented as tan θ.
• cosecant: It is the reciprocal of sin θ and is represented as cosec θ.
• secant: It is the reciprocal of cos θ and is represented as sec θ.
• cotangent: It is the reciprocal of tan θ and is represented as cot θ.

According to the above image, Trigonometric Ratios are

• sin θ = Perpendicular/Hypotenuse = AB/AC
• cos θ = Base/Hypotenuse = BC/AC
• tan θ = Perpendicular/Base = AB/BC
• cosec θ = Hypotenuse/Perpendicular = AC/AB
• sec θ = Hypotenuse/Base = AC/BC
• cot θ = Base/Perpendicular = BC/AB

Trigonometry is a discipline of mathematics that studies the relationships between the lengths of the sides and angles of a right-angled triangle. Trigonometric functions, also known as goniometric functions, angle functions, or circular functions, are functions that establish the relationship between an angle to the ratio of two of the sides of a right-angled triangle. The six main trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometric angles are the Angles defined by the ratios of trigonometric functions. Trigonometric angles represent trigonometric functions. The value of the angle can be anywhere between 0-360°.

As given in the above figure in a right-angled triangle:

• Hypotenuse: The side opposite to the right angle is the hypotenuse, It is the longest side in a right-angled triangle and opposite to the 90° angle.
• Base: The side on which angle C lies is known as the base.
• Perpendicular: It is the side opposite to angle C in consideration.