Question

Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and . Find the exact values of the five

Answer 1

Given:

`\cot \theta=-(2)/(17)`

And θ is an angle in the standard position whose terminal side is in Quadrant IV.

We know that,

`\cot \theta=\frac{\text{adjacent side}}{\text{opposite side}}`

Hence, opposite side=17 and adjacent side=2

Using pythogoras theorem,

`\begin{gathered} \text{Hyp}^2=\text{Opp}^2+\text{Adj}^2 \\ \text{Hyp}^2=17^2+2^2 \\ \text{Hyp}^2=289+4 \\ \text{Hyp}^2=293 \\ \text{Hyp}=\sqrt[]{293} \end{gathered}`

Then the other values are,

Since θ lies in IV quadrant.

cos and sec values are positve and the others have negative values.

So,

`\begin{gathered} \sin \theta=-(opp)/(hyp) \\ =-\frac{17}{\sqrt[]{293}} \\ \cos \theta=(adj)/(hyp) \\ =\frac{2}{\sqrt[]{293}} \\ t\text{an }\theta=-\frac{\text{opp}}{\text{adj}} \\ =-(17)/(2) \\ co\sec \theta=-(hyp)/(opp) \\ =-\frac{\sqrt[]{293}}{17} \\ \sec \theta=\frac{hyp}{\text{adj}} \\ =\frac{\sqrt[]{293}}{2} \end{gathered}`

Hence, the correct option is B.