Answer:
Explanation:
Let us sketch the angle ø.
As can be seen from the triangle above,
[tex]\sin\phi=-\frac{1}{2}[/tex]Furthermore,
[tex]\tan\phi=-\frac{1}{x}[/tex]we just need to find the value of x.
To find the value of x, we use pythagoras's theorem.
[tex]x^2+1^2=2^2[/tex][tex]x^2+1=4[/tex]subtracting 1 from both sides gives
[tex]x^2=4-1[/tex][tex]x^2=3[/tex]taking the sqaure root of both sides gives
[tex]x=\sqrt{3}[/tex]with the value of x in hand, we now have
[tex]\tan(\phi)=-\frac{1}{x}=-\frac{1}{\sqrt{3}}[/tex][tex]\boxed{\tan\phi=-\frac{1}{\sqrt{3}}.}[/tex]which is our answer!
