Question

Solve (Sin15degree + iCos15degree)3

Answer 1

try to type it in equation form or draw it

Answer 2

\[e^{i\theta}=\cos \theta + i \sin \theta\]

Answer 3

wait lemme get home now

Answer 4

\[\large\left(\sin(15^\circ)+i\cos(15^\circ)\right)^3=\left(e^{i\cdot15^\circ}\right)^3=\left(e^{i\frac{\pi}{12}}\right)^3\\\large=e^{i\frac{\pi}{4}}=\sin\left(\frac{\pi}{4}\right)+i\cos\left(\frac{\pi}{4}\right)\]

Answer 5

Similarly, you can apply de Moivre's formula directly:
\[\large\left(\sin\theta+i\cos\theta\right)^3=(\sin(3\theta)+i\cos(3\theta))\]