Substitute this (1 Viewer)

[housemouse]

If you substitute x = pi/4 and x =0 into sin ^n-1 x , what would you get?

 

[icycloud]

For x = pi/4,

y = Sin[pi/4]^(n-1)
= (1/Sqrt[2])^(n-1)
= 1/Sqrt[2]^(n-1)

(And you can rationalise the denominator if you want.)

For x = 0,

y = Sin[0]^(n-1)
= 0^(n-1)
= 0

 

[shimmerz_777]

what is the context of that questiuon? was it like a reoccurence formula or something, cause it didnt seem very complex on its own

 

[housemouse]

It was part of a reduction question, I just got confused with that part so i couldnt finish the rest of the question

 

[Rax]

Ah Reduction questions

Usually keep me busy

And yep if you stuff up one question the rest of it becomes pretty impossible

On a Side note my friend was trying to create an equation of integrating (Sinx)^n and (Cosx)^n

It ended quite humerously

GG

 

[shimmerz_777]

you can find a reoccurence formula for intergral of (cosx)^n in the fitzpatric book if your friend wants it

 

[Trev]

You use parts with (cosx).(cosx)^n-1 from memory.

 

[_ShiFTy_]

Has there ever been a question where you had to make your own reduction formula instead of showing that its equal to something. Cos when you have the answer that you are trying to get, its much much easier.

 

[Riviet]

I've been told that you will nearly always be given what to show for reduction formula questions, except in those where you're asked to evaluate something like I₄.