Alan

For 1 see https://web2.0calc.com/questions/let-f-x-be-a-polynomial-such-that-f-0-4-f-1-5-and_1#r2

Let f(x) be a polynomial such that f(0) = 4, f(1) = 5, and f(2) = 10. Find the remainder when f(x) is divided by x(x - 1)(x - 2).

Hmm, surprisingly, it does work for pi/45:

The answer is 97, but I cheated and used a piece of software to find it!  (You could use Wolfram Alpha).

Try x = 2, y = 1, z = 1/2

I'm going to assume you mean the angle to be \(\frac{\pi}{5}\).

Are you sure you don't mean \(\sin^2(\frac{\pi}{5})\) ?

As follows:

If I draw four cards from a deck of 52 cards, what is the probability that I will have one card of every suit?

First card:                p1 = 1;

Second card           p2 = 39/51

Third card               p3 = 26/50

Fourth card            p4 = 13/49

Overall probability = p1*p2*p3*p4 

I'll leave you to do the number crunching.

Here's one way of doing this: