Thread: Pre-Calc Homework Question

1. Pre-Calc Homework Question

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!

2. Re: Pre-Calc Homework Question

Originally Posted by jonathanraxa
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 \begin{align*} \theta^{\circ} \end{align*}, then the other angle is \displaystyle \begin{align*} 90^{\circ} - \theta^{\circ} \end{align*}. Do you understand why? The three angles in a triangle have to add to \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 \begin{align*} \sin{\left(90^{\circ} - \theta^{\circ}\right)} = \cos{\theta^{\circ}} \end{align*} and \displaystyle \begin{align*} \cos{\left(90^{\circ} - \theta^{\circ}\right)} = \sin{\theta^{\circ}} \end{align*}.

3. Re: Pre-Calc Homework Question

Ok I got that thanks. As for the second portion, given that:
t=sin(18degrees)
what are the steps in solving:
(8t^4)-(8t^2)-t+1=0 ?

4. Re: Pre-Calc Homework Question

Originally Posted by jonathanraxa
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!
What is t being used to represent?

5. Re: Pre-Calc Homework Question

I'm plugging sin(18degrees) in for t in the equation.

6. Re: Pre-Calc Homework Question

I want to find out how this is true. I don't know where to begin =/