Expert: Scotto - 3/27/2008

Question
The question is..

Use the sum and difference formulas and the sin2x and cos2x to express sinx^0 where x is an integer between 0 and 90, in terms of rational numbers and radicals for as many values of x as possible.

I am confused about expressing it in rational numbers and radicals. Please show me how to do that.

Also, I know that anything to the power of 0 is 1, and sin1 is 0 in radians.. that makes expressing it in rational numbers and radicals even more confusing.. please help me..

Please reply to me asap! Thank you

Answer
This is what I read, written in proper mathematical notation:

 Use the sum and difference formulas and the sin(2x) and cos(2x)
 to express sin(x^0) where x is an integer between 0 and 90, in
 terms of rational numbers and radicals for as many values of x
 as possible.

The only mistake I see is in computation of sin(1), as you will see at the end of the next paragraph.

The way the problem is stated, I don't understand where the sin(2x) or cos(2x) come into play when we are approximating sin(x^0).  As you have stated, x^0 = 1.  If x is in radians or degrees, the sin(1) is not zero, however.

It is known that sin(2x)=2sin(x)cos(x) and that
cos(2x) = cos^2(x) - sin^2(x).

It is also known that pi radians = 180 degrees.

Rational numbers are any number that can be expressed as a/b where a and b are integers.

Radical numbers are anything like this with roots involved (square root,cube root, etc).