# Binomial Theorem?

• May 7th 2010, 12:10 PM
yobacul
Binomial Theorem?
Expand (2 - 5sinx)^-4 in ascending powers of sin x up to and including the term in (sinx)^3. FInd the complete set of values of x in the interval 0 < x < 360 for which the expansion is valid.

Can I let sin x be equal to some letter, use binomial and then back substitute? Thanks.
• May 7th 2010, 12:16 PM
e^(i*pi)
Quote:

Originally Posted by yobacul
Expand (2 - 5sinx)^-4 in ascending powers of sin x up to and including the term in (sinx)^3. FInd the complete set of values of x in the interval 0 < x < 360 for which the expansion is valid.

Can I let sin x be equal to some letter, use binomial and then back substitute? Thanks.

Using a substitute is fine although I think there is a typo in your equation, are you sure the exponent is -4 and not 4?
• May 7th 2010, 12:20 PM
yobacul
Binomial
It is -4 yes, not 4. That's why I thought of binomial, since binomial can be used with negative powers, no? Or could one use the Maclaurin?
• May 7th 2010, 12:27 PM
e^(i*pi)
Quote:

Originally Posted by yobacul
It is -4 yes, not 4. That's why I thought of binomial, since binomial can be used with negative powers, no? Or could one use the Maclaurin?

The binomial theorem can be used to expand it but I don't see how it can be used to get a $\displaystyle \sin^3(x)$ term.
• May 7th 2010, 12:30 PM
yobacul
I think since you let sin x = y, and then use the binomial till y^3 and then backsubstitute to get (sin x)^3