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Question

# The equation Tan $\theta=1$ describes the counterclockwise angle through which a flywheel rotates in 1 millisecond. Through how many degrees has the flywheel rotated after 25 milliseconds?

Solution

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Step 1
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Transfer the $\tan$ to right side to get the equation in terms of theta,

$\theta=\tan^{-1}(1)$

The range of principal values of $\tan^{-1}$ is $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$ so the positive value of $\tan^{-1}$ must be lies between $0$ and $\dfrac{\pi}{2}$.Therefore,

$\theta=45^o$

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