Given that tan 0=-1, what is the value of sec 0, for 3pi/2 < 0 < 2pi?

√2

Step-by-step explanation:

Given tanθ = -1

θ = arctan(-1)

θ = -45°

Since tan θ is negative in the 2nd and 4th quadrant,

New angles:

θ = 90-45 = 45°(2nd quadrant)

θ = 360-45 = 315° (4the quadrant)

To get secθ between 3π/2< θ<2π

In trigonometry identity,

secθ = 1/cosθ

We will use θ = 315° since it is the only angle that falls within the given range

Sec315° = 1/cos315°

Sec315° = 1/(1/√2)

Sec 315° = √2