Step-by-step explanation:
[tex]\tan(\theta) = -1 , \frac{3\pi}{2}<\theta<2\pi[/tex]
which is in 4ᵗʰ quadrant ( where only cosine and secant are positive)
now,
in short, you can see where
[tex]\tan(\theta) = 1[/tex]
, in 1ˢᵗ quadrant, which is \frac{\pi}{4} and subtract that from
[tex]2\pi[/tex]
so
[tex]\theta =\frac{7\pi}{4}[/tex]
now ,
[tex]\cos(\theta) =\cos(\frac{7\pi}{4})=\frac{1}{\sqrt2}[/tex]
[making the triangle in the fourth quadrant]
