Question

Which of the following represents vector t = –8i + 6j in trigonometric form?

Answer 1

yup it is the second option

Explanation:

Answer 2

The vector is given to be:

`t=-8i+6j`

For a vector v given to be:

`v=ai+bj`

the trigonometric form is given to be:

`v=|v|\langle\cos \theta,\sin \theta\rangle`

where

`|v|=\sqrt[]{a^2+b^2}`

and

`\theta=\tan ^(-1)(b)/(a)`

Comparing this to our vector, we have:

`\begin{gathered} a=-8 \\ b=6 \end{gathered}`

Therefore,

`\begin{gathered} |t|=\sqrt[]{(-8)^2+6^2}=\sqrt[]{64+36}=\sqrt[]{100} \\ |t|=10 \end{gathered}`

and

`\begin{gathered} \theta=\tan ^(-1)((6)/(-8))=_{}\tan ^(-1)(-(6)/(8))_{} \\ \theta=-36.87 \end{gathered}`

Since the angle is negative, we can add 180° to the angle to get the positive angle. Therefore:

`\theta=-36.87+180=143.13`

Therefore, the vector in trigonometric form will be:

`t=10\langle\cos 143.13,\sin 143.13\rangle`

The correct option is the SECOND OPTION.