ANSWER:
3rd option
[tex]w=37(\cos 341.075\degree,\sin 341.075\degree)[/tex]
STEP-BY-STEP EXPLANATION:
Given:
w = 35i - 12j
We know that the trigonometric form is given as follows:
[tex]w=|w|\cdot(\cos \theta,\sin \theta)[/tex]
The first thing is to calculate the normal of the vector, just like this:
[tex]\begin{gathered} |w|=\sqrt[]{35^2+(-12)^2} \\ |w|=\sqrt[]{1225+144} \\ |w|=\sqrt[]{1369} \\ |w|=37 \end{gathered}[/tex]
Now, we calculate the value of the angle by means of the sine, just like this:
[tex]\begin{gathered} \sin \theta=\frac{-12}{37} \\ \theta=\sin ^{-1}_{}\mleft(\frac{-12}{37}\mright) \\ \theta=18.925 \\ \theta=360-18.925 \\ \theta=341.075\degree \end{gathered}[/tex]
Therefore, the vector w in its trigonometric form is as follows:
[tex]w=37(\cos 341.075\degree,\sin 341.075\degree)[/tex]
