Answer:
[tex]\cos \theta=-\frac{1}{\sqrt{5}}[/tex]
Step-by-step explanation:
[tex]Given\ \tan \theta=-2\ \ \ \ \ -\frac{\pi}{2}<\theta<\pi[/tex]
Hence [tex]\theta[/tex] is in second quadrant.
[tex]\tan \theta=\frac{opposite}{adjacent}=-2\\\\Length\ of\ opposite=2,\ \ Length\ of\ adjacent=1\\[/tex]
Pythagorean Theorem:[tex]hypotenuse^2=opposite^2+adjacent^2[/tex]
[tex]hypotenuse^2=(1)^2+(2)^2=1+4=5\\hypotenuse=\sqrt{5}[/tex]
[tex]\cos \theta=\frac{adjacent}{hypotenuse}\\\\\cos \theta=\frac{1}{\sqrt{5}}[/tex]
But in the second quadrant [tex]\cos \theta[/tex] will be negative.
Hence
[tex]\cos \theta=-\frac{1}{\sqrt{5}}[/tex]
