Chapter EP, Problem 13.1.3EP

To determine

To find: The value of the six trigonometric function of $\theta$

Answer to Problem 13.1.3EP

The value of the six trigonometric function of $\theta$ are shown below.

Explanation of Solution

Given information: The figure is shown below.

Calculation:

Consider the equation.

$\begin{array}{c}c=\sqrt{a^2+b^2}\\ c=\sqrt{{\left(10\right)}^2+{\left(2\sqrt{3}\right)}^2}\\ =10.58\end{array}$

The six trigonometric ratio of the function of $\theta$ are,

$\begin{array}{l}\sin \theta =\frac{2\sqrt{3}}{10.58}\\ \cos \theta =\frac{10}{10.58}\\ \tan \theta =\frac{2\sqrt{3}}{10}\\ \cot \theta =\frac{10}{2\sqrt{3}}\\ \csc \theta =\frac{10.58}{2\sqrt{3}}\\ \sec \theta =\frac{10.58}{10}\end{array}$