A problem from my homework:
Explain why sin(18degrees)=cos(72degrees). Then using the previous problem, explain why:
(8t^4)-(8t^2)-t+1=0
Thank You!
Draw any right-angle triangle. Call one of the non-right angles $\displaystyle \displaystyle \begin{align*} \theta^{\circ} \end{align*}$, then the other angle is $\displaystyle \displaystyle \begin{align*} 90^{\circ} - \theta^{\circ} \end{align*}$. Do you understand why? The three angles in a triangle have to add to $\displaystyle \displaystyle \begin{align*} 180^{\circ} \end{align*}$.
Now note that from the point of view of each angle, the hypotenuses are the same, but the opposite and adjacent sides switch.
So $\displaystyle \displaystyle \begin{align*} \sin{\left(90^{\circ} - \theta^{\circ}\right)} = \cos{\theta^{\circ}} \end{align*}$ and $\displaystyle \displaystyle \begin{align*} \cos{\left(90^{\circ} - \theta^{\circ}\right)} = \sin{\theta^{\circ}} \end{align*}$.