What is the Correct Method for Finding Induced EMF in a Coil?

[ReidMerrill]

Homework Statement

A 4.0 cm diameter coil (1000 turns) is at rest in the XY plane. The magnetic field in this region of space is given by B=(0.30i + 0.50t² k) What is the induced EMF in the coil at t=2.0 seconds

Homework Equations

ε=dΦ/dt
Φ=ABcosθ

The Attempt at a Solution

ε=[/B]d/dt( πr²)(0.03i+0.5t² k) Cosθ
ε=πr²cosθ *0.5*2t k

Using trig I found θ=59° and plugging in the numbers I got ε=0.00129V k

I assume I did something wrong. Is this anywhere close to the proper method?

 

[NascentOxygen]

You need to first sketch the correct diagram! Draw a circle, and position your co-ordinate system inside that circle (the ring) appropriately.