Holiday homeworkk

[mandy]

Oh I understand now, thank you guys!

[mandy]

I have a problem with this one:

Prove:

[zzdfa]

remember that identity


use it here.

The mnemonic 'SOP' -> 'same opposite positive' is useful to remember what the signs should be for that factorization. The first sign should be the same as the one in between x^3 and y^3 in the expression on the left, the 2nd sign should be opposite, the last one is always positive.



also use '\sin' not 'sin' in LaTeX.
vs

[qshyrn]

(sinx)^3 +(cosx)^3= (sinx+cosx) ((sinx)^2  - sinxcosx+ (cosx)^2) = (sinx+cosx) (1-sinxcosx) _-- combining the cosx sqrd and the the sinx sqrd to get the 1

EDIT: BEATEN BY THE GUY ABOVE ME

[mandy]

THANKS ALOT GUYS <3

[kamil9876]

the way I like to remember that identity is:


has a solution , hence is a factor. And if all signs were + we would have too many in the expansion.

[mandy]

For this one, am I doing it right?

sin⁶x + cos⁶x = 1 - 3sin²xcos²x

Working out:

I used: x⁶ + y⁶ = (x² + y²)(x⁴ - x²y² + y⁴)
So I got (sin²x + cos²x)(sin⁴x - sin²xcos²x + cos⁴x)
(sin²x + cos²x) ; that turns into 1, so multiples in and disappears.
Then, what do I do with this bit : (sin⁴x - sin²xcos²x + cos⁴x)?

[Damo17]

For this one, am I doing it right?

sin⁶x + cos⁶x = 1 - 3sin²xcos²x

Working out:

I used: x⁶ + y⁶ = (x² + y²)(x⁴ - x²y² + y⁴)
So I got (sin²x + cos²x)(sin⁴x - sin²xcos²x + cos⁴x)
(sin²x + cos²x) ; that turns into 1, so multiples in and disappears.
Then, what do I do with this bit : (sin⁴x - sin²xcos²x + cos⁴x)?

yes you are doing it right.

from the last bit sub in and to get:



which gives

[mandy]

which gives

Thank you, but for this bit, I can't see how it simplifies to give 1 - 3cos²xsin²x :S

[Cataclysmic]

Expand the brackets and add them together and use sin^2(x)+cos^2(x) = 1

[mandy]

Okay, I get it now, thanks a lot <3

[mandy]

DOUBLE ANGLE FORMULAE

Find x such that:

4sinx^o = secx^o, 0^o<x<360^o

- Note: These signs "< " are meant to be less than or equal to signs, but I don't know how to make them :[

[crappy]

4sinx= 1/cosx

4sinx*cosx=1

2( 2sinxcosx) = 1

2(sin2x)= 1

sin2x= 1/2

Basic angle= pi/6................ becomes basic now

cbf latex lol

[mandy]

okay, thank you.

[Cataclysmic]

DOUBLE ANGLE FORMULAE

Find x such that:

4sinx^o = secx^o, 0^o<x<360^o

- Note: These signs "< " are meant to be less than or equal to signs, but I don't know how to make them :[

Code: [Select]

[tex]\leq[/tex]Kind of like l = less, eq = equal

Code: [Select]

[tex]\geq[/tex]