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{(1)/(3)}{\sqrt[]{(-(1)/(5))^2+((1)/(3))^2}}`

`\begin{gathered} \cos \theta=\frac{(1)/(3)}{\sqrt[]{(1)/(25)+(1)/(9)}} \\ \cos \theta=\frac{(1)/(3)}{\sqrt[]{(25+9)/(25*9)}} \end{gathered}`
`\begin{gathered} \cos \theta=\frac{(1)/(3)*\sqrt[]{25*9}}{\sqrt[]{34}} \\ \cos \theta=\frac{(1)/(3)*5*3}{\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=(1)/(\tan \theta)=(1)/((y)/(x)) \\ \cot \theta=(x)/(y) \end{gathered}`
`\cot \theta=(5)/(9)`

so the correct answer is option D