Question

define Trigonometric
ratios (sin, cos, tan, cot, sec, cosec) with 3 examples.​

Answer 1

Step-by-step explanation:

In mathematics, the trigonometric 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.

Answer 2

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⭕⭕⭕⭕⭕➡️➡️➡️➡️Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.⬅️⬅️⬅️⬅️⭕⭕⭕⭕⭕

⭕Sine Function⭕

➡️Sine function of an angle is the ratio between the opposite side length to that of the hypotenuse. From the above diagram, the value of sin will be:

➡️Sin a =Opposite/Hypotenuse = CB/CA

⭕Cos Function⭕

➡️Cos of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. From the above diagram, the cos function will be derived as follows.

➡️Cos a = Adjacent/Hypotenuse = AB/CA

⭕Tan Function⭕

➡️The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio. From the diagram taken above, the tan function will be the following.

➡️Tan a = Opposite/Adjacent = CB/BA

➡️Also, in terms of sine and cos, tan can be represented as:

➡️Tan a = sin a/cos a

⭕Secant, Cosecant and Cotangent Functions⭕

➡️Secant, cosecant (csc) and cotangent are the three additional functions which are derived from the primary functions of sine, cos, and tan. The reciprocal of sine, cos, and tan are cosecant (csc), secant (sec), and cotangent (cot) respectively. The formula of each of these functions are given as:

➡️Sec a = 1/(cos a) = Hypotenuse/Adjacent = CA/AB

➡️Cosec a = 1/(sin a) = Hypotenuse/Opposite = CA/CB

➡️cot a = 1/(tan a) = Adjacent/Opposite = BA/CB

❣Note: Inverse trigonometric functions are used to obtain an angle from any of the angle’s trigonometric ratios. Basically, inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions are represented as arcsine, arccosine, arctangent, arccotangent, arcsecant, and arc cosecant.❣