Given:
[tex]tan\theta=-0.3573[/tex]Aim:
[tex]We\text{ need to find the value of }\theta.[/tex]Explanation:
[tex]tan\theta=-0.3573[/tex]Taking inverse trigonometry on both sides.
[tex]tan^{-1}tan\theta=tan^{-1}(-0.3573)[/tex][tex]\theta=tan^{-1}(-0.3573)[/tex][tex]\theta=-19.6618087737[/tex][tex]\theta\approx-19.6618[/tex]We know that
[tex]tan(180+\theta)=tan\theta[/tex][tex]tan(180-19.6618)=tan(-19.6618)[/tex][tex]tan(160.3382)=tan(-19.6618)[/tex]The angels are
[tex]-19.6618\text{ and 160.3382}[/tex]Final answer:
[tex]\theta=19.6618,160.3382[/tex]