# How to calculate sin/cos/tan of a Quaternion?

Most of the article was not hard to understand, except the (Exponential, logarithm, and power) part.

To calculate the exponential, I have to calculate sin/cos of the imaginary part, but that functions aren't defined on Quaternions (in the article).

As you can see in the answer cited in the comment, the exponential of a quaternion $z=a+b\mathbf{i}+c\mathbf{j}+d\mathbf{k} = a+\mathbf{v}$, is:
$$e^z = e^{a+\mathbf{v}}=e^a \left( \cos |\mathbf{v}| +\dfrac{\mathbf{v}}{|\mathbf{v}|} \,\sin |\mathbf{v}| \right)$$
where $|\mathbf v|= \sqrt{b^2+c^2+d^2}$ is a real number (the modulus of $\mathbf v$), so $\cos |\mathbf{v}|$ and $\sin |\mathbf{v}|$ are well known trigonometric function of a real number, and they have nothing to do with $\cos$ and $\sin$ of a quaternion.