Why Does the Trigonometric Function in the FEM Calculation Differ?

[LCSphysicist]

Homework Statement

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Relevant Equations

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I need to find the FEM induced in a coil that rotates around the y-axis and is inside a solenoid. The coil starts in the plane yz
$r$ is the radius of the coil
$n$ is the number of spiral by length of the solenoid.
$N$ is the number of turns of the coil
$w$ is the angular velocity that the coils rotate.
$I$ is the current passing through the solenoid

I just thought this:
$$\phi = \langle B,A \rangle = \mu n I \pi r^2 N cos(\theta = wt)$$
$$ \epsilon = -\dot \phi = \mu n I \pi r^2 N w sin(\theta = wt)$$

This is a simple exercise. But i can't see why my answer is wrong. That is, the answer provided by the list is $\mu n I \pi r^2 N w cos(\theta = wt)$. The trignometric function is different. My answer says that at t=0 the induced FEM is zero, the other says it is maximum.

 

[berkeman]

Sorry, what's FEM?

 

[Orodruin]

Which axis is given as the solenoid’s symmetry axis? This is a vital piece of information. This is why you are asked to provide the homework statement verbatim, which you have ignored.

Sorry, what's FEM?

Based on context, I would assume the OP is not a native English speaker and the original language is a Latin language. FEM would really be EMF, electromotive force.

 

[kuruman]

My answer says that at t=0 the induced FEM is zero, the other says it is maximum.

Is your definition of variable $\theta$ the same as the definition in the "other"? If yours differs by 90^o from the "other", then that could be the source of the disagreement.