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

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet