define trignometrical ratios
Answers
Answer: It is defined as the values of all the trigonometric function based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle. Consider a right-angled triangle, right-angled at B.
Trigonometric ratios
With respect to ∠C, the ratios of trigonometry are given as:
sine: Sine of an angle is defined as the ratio of the side opposite(perpendicular side) to that angle to the hypotenuse.
cosine: Cosine of an angle is defined as the ratio of the side adjacent to that angle to the hypotenuse.
tangent: Tangent of an angle is defined as the ratio of the side opposite to that angle to the side adjacent to that angle.
cosecant: Cosecant is a multiplicative inverse of sine.
secant: Secant is a multiplicative inverse of cosine.
cotangent: Cotangent is the multiplicative inverse of the tangent.
The above ratios are abbreviated as sin, cos, tan, cosec, sec and tan respectively in the order they are described. So, for Δ ABC, the ratios are defined as:
sin C = (Side opposite to ∠C)/(Hypotenuse) = AB/AC
cos C = (Side adjacent to ∠C)/(Hypotenuse) = BC/AC
tan C = (Side opposite to ∠C)/(Side adjacent to ∠C) = AB/AC = sin ∠C/cos ∠C
cosec C= 1/sin C = (Hypotenuse)/ (Side Opposite to ∠C) = AC/AB
sec C = 1/cos C = (Hypotenuse)/ (Side Opposite to ∠C) = AC/BC
cot C = 1/tan C = (Side adjacent to ∠C)/(Side opposite to ∠C)= BC/AB
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Answer......✏
In mathematics, the trigonometric functions called circular functions, angle functions or goniometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.