Question

I looked this up on wolfram alpha to check the derivative, graph, etc but I thought you couldn't put sin or cos to the power of something... :/ (referring to the derivative :P )

how would you rearrange that so that there is no sin^( ) or cos^( ) ?

https://www.wolframalpha.com/input/?i=sin%5E5+alpha+cos%5E5+alpha

thank you:) above is the link of the inputted function :)

Answer 1

you can put sin^5 alpha and cos^5 alpha properly.
you did get its derivative too.
what are you confused with ?
(if you're confused, you can put 'x' instead of alpha in wolf)

Answer 2

http://www.math.msu.edu/~shapiro/Teaching/classes/425/exp_n_sin.pdf

Answer 3

oh did i not enter it in correctly? i'm trying to put this... \[\sin^5 \alpha \cos^5 \alpha\] i meant because in the derivative, it says\[5\sin^4\] etc.... how would you make it so that there is no sin^4 ? or is that the only way?

Answer 4

it says the derivative is \[5\sin^4 \alpha \cos^4 \alpha \cos(2 \alpha)\]

would i be able to rewrite it like this? is this the same thing? \[5\sin(1)^4 \alpha \cos(1)^4 \alpha \cos (2 \alpha)\]

Answer 5

are you not comfortable with exponents of sin/cos ?
\(\sin x \times \sin x = \sin^2 x \)

\(\alpha\) is just another variable like x
\(\sin (1)^4 \alpha\) is totally different from \(\sin^4 \alpha \)

Answer 6

ohh okay i see now...

so if i were to rewrite it without the exponent, it would have to look like this? \[5 * \sin \alpha * \sin \alpha * \sin \alpha * \sin \alpha * \cos \alpha * \cos \alpha *\cos \alpha *\cos \alpha * \cos(2\alpha)\] is this equivalent to what is written in wolfram alpha?

Answer 7

yes. thats correct.
but that form would never be used as an answer...why use long form when we can write it in short nicely :)

Answer 8

oh and would \[\sin^4 \alpha \] be equivalent to \[(\sin (\alpha ))^4 \] or \[\sin (\alpha) ^4\] ?

Answer 9

ohh okay:)

yeah shorter is better hehe.. just wanted to make sure that i understood the exponent thingy :)

Answer 10

\(\sin ^4 \alpha = (\sin \alpha)^4\)

Answer 11

\(\sin \alpha^4 = \sin (\alpha \times \alpha \times \alpha \times \alpha)\)

Answer 12

ohhh so this would be the same thing?

\[\sin(\alpha^4)\]

Answer 13

these 2 are different things
\(\sin ^4 \alpha = (\sin \alpha)^4= \sin \alpha \times \sin \alpha \times \sin \alpha \times \sin \alpha \)
\(\sin \alpha^4 = \sin (\alpha \times \alpha \times \alpha \times \alpha)\)

Answer 14

oh okay... darn.. so if i were to write it like this, would it be interpreted as \[\sin^4 \alpha\]? one of those? or both? :/