Chapter 12.4, Problem 4ST

To determine

When angle $\theta$ is in standard position, its terminal side passes through $\left(\sqrt{7},3\right)$ . We have to find values of the sic trigonometric function of $\theta$

Explanation of Solution

Given information :

Given point $\left(\sqrt{7},3\right)$

  

From the figure we can deduce that the length of AB=3 units

Length of OB $=\sqrt{7}$ units.

Length of OA is $\sqrt{{\left(\sqrt{7}\right)}^2+{\left(3\right)}^2}=\sqrt{16}=4$

Therefore,

  $\begin{array}{l}\sin \theta =\frac{AB}{OA}=\frac{3}{4}\\ \csc \theta =\frac{1}{\sin \theta }=\frac{4}{3}\\ \cos \theta =\frac{OB}{OA}=\frac{\sqrt{7}}{4}\\ \sec \theta =\frac{1}{\cos \theta }=\frac{4}{\sqrt{7}}\\ \tan \theta =\frac{BA}{OB}=\frac{3}{\sqrt{7}}\\ \cot \theta =\frac{\sqrt{7}}{3}\end{array}$