Question

Trigonometry Functions of Any Angle CAA point on the terminal side of angle O is given. Find the exact value of the indicated trigonometric function of e.1) (12, 16) Find csc 0.I need help with 4,5and 6

Answer 1

4) the point is (x, y) = (-1/5, 1/3)

so the value of cos is

$\cos \theta=\frac{y}{\sqrt[]{x^2+y^2}}$

put the values,

$\cos \theta=\frac{\frac{1}{3}}{\sqrt[]{(-\frac{1}{5})^2+(\frac{1}{3})^2}}$

$\begin{gathered} \cos \theta=\frac{\frac{1}{3}}{\sqrt[]{\frac{1}{25}+\frac{1}{9}}} \\ \cos \theta=\frac{\frac{1}{3}}{\sqrt[]{\frac{25+9}{25\times9}}} \end{gathered}$$\begin{gathered} \cos \theta=\frac{\frac{1}{3}\times\sqrt[]{25\times9}}{\sqrt[]{34}} \\ \cos \theta=\frac{\frac{1}{3}\times5\times3}{\sqrt[]{34}} \\ \cos \theta=\frac{5}{\sqrt[]{34}} \end{gathered}$$\cos \theta=\frac{5\sqrt[]{34}}{34}$

so the correct answer is option B

5)

$\begin{gathered} \cot \theta=\frac{1}{\tan \theta}=\frac{1}{\frac{y}{x}} \\ \cot \theta=\frac{x}{y} \end{gathered}$$\cot \theta=\frac{5}{9}$

so the correct answer is option D