Question

If tan(0)=-1 and 3 pi/2< 0< 2 pi, what is cos(0)?

Answer 1

Explanation:

`\tan(\theta) = -1 , (3\pi)/(2)<\theta<2\pi`

which is in 4ᵗʰ quadrant ( where only cosine and secant are positive)

now,

in short, you can see where

`\tan(\theta) = 1`

, in 1ˢᵗ quadrant, which is \frac{\pi}{4} and subtract that from

`2\pi`

so

`\theta =(7\pi)/(4)`

now ,

`\cos(\theta) =\cos((7\pi)/(4))=(1)/(\sqrt2)`

[making the triangle in the fourth quadrant]