What are the 6 Trig Functions?

Answer – The six trigonometric functions are sine (sin), cosine (cos), tangent (tan), secant (sec), cosecant (cosec), and cotangent (cot).

Explanation:

The 6 trig functions for an angle of a right triangle can be found using its opposite side, its adjacent side, and the hypotenuse.

Consider the following right triangle XYZ, where X is the angle whose trig functions need to be found.

Right triangle XYZ with angle X having opposite side a, adjacent side c, and hypotenuse b

The opposite side of X is a, and its adjacent side is c. The hypotenuse (side opposite the right angle) is b. Therefore, the trigonometric functions of X are as follows:

$\sin x = \frac{o p p o s i t e s i d e}{h y p o t e n u s e} = \frac{a}{b}$

$\cos x = \frac{a d j a c e n t s i d e}{h y p o t e n u s e} = \frac{c}{b}$

$\tan x = \frac{\sin x}{\cos x} = \frac{o p p o s i t e s i d e}{a d j a c e n t s i d e} = \frac{a}{c}$

$\cos e c x = \frac{1}{\sin x} = \frac{h y p o t e n u s e}{o p p o s i t e s i d e} = \frac{b}{a}$

$s e c x = \frac{1}{\cos x} = \frac{h y p o t e n u s e}{a d j a c e n t s i d e} = \frac{b}{c}$

$c o t x = \frac{1}{\tan x} = \frac{a d j a c e n t s i d e}{o p p o s i t e s i d e} = \frac{c}{a}$

The measures of the sides of a given right triangle can be substituted in the relevant formulas to find the trigonometric functions of an angle.

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Answer – The six trigonometric functions are sine (sin), cosine (cos), tangent (tan), secant (sec), cosecant (cosec), and cotangent (cot).

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