Thread: 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.

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?

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?

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 term.

I think since you let sin x = y, and then use the binomial till y^3 and then backsubstitute to get (sin x)^3