Relations between functions of the same arc

Mathematics

Know the main relationships between functions of the same arc, defined from the sine and cosine functions.

Per Elainy MarcianoPosted in 12/11/2020 - 16:10

To share

From the functions sine and cosine of the same arc, other trigonometric functions: tangent, secant, cosecant and cotangent.

See below the main relations between functions of the same arc.

Students from Rio de Janeiro will compete for medals at the Olympics…

The Institute of Mathematics is open for registration for the Olympics…

Tangent is defined as the ratio of sine and cosine.

$\dpi{120} \boldsymbol{tan (x) \frac{sin (x)}{cos (x)}}$

As there is no division by zero, only the values of $\dpi{120} x$ for which $\dpi{120} cos (x)\neq 0$ .

Therefore, we must have $\dpi{120} \boldsymbol{x\neq \frac{\pi}{2}+ k \pi, k\in \mathbf{Z}}$ .

The secant is defined as the inverse of the cosine function:

$\dpi{120} \boldsymbol{sec (x) \frac{1}{cos (x)}}$

Being $\dpi{120} \boldsymbol{x\neq \frac{\pi}{2}+ k \pi, k\in \mathbf{Z}}$ .

The cosecant is defined as the inverse of the sine function:

$\dpi{120} \boldsymbol{csc (x) \frac{1}{sin (x)}}$

For what $\dpi{120} sin (x)\neq 0$ , we should have $\dpi{120} \boldsymbol{x\neq k \pi, k\in \mathbf{Z}}$ .

The cotangent is given by the inverse of the tangent function:

$\dpi{120} \boldsymbol{cot (x) \frac{1}{tan (x)} \frac{cos (x)}{sin (x)}}$

Being $\dpi{120} \boldsymbol{x\neq k \pi, k\in \mathbf{Z}}$ .

You may also be interested:

Trigonometry

To share

on Jul 22, 2021