establishing identities with ^3 and ^4 in them  TOPIC_SOLVED

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.

establishing identities with ^3 and ^4 in them

Postby bikeman on Thu Jun 10, 2010 12:07 am

i am asked two similar problems. my question is how it was done as the example in the book i am reading is useless in explaining.
the first question is:
(sin^3t+cos^3t)/(sint+cost)=1-sint cost
the example plays out to what i assume is factoring sint+cost out of it to look like (sint+cost)(sin^2t-sint cost+cos^2)/(sint+cost)

my question is, where did the "sin^2t-sint cost+cos^2" come from? when i factor it it doesnt look like that.

the next problem is (cos^4t-sin^4t)/(cos[2t]) how do i get rid of the ^4?


thanks for any help provided.
bikeman
 
Posts: 2
Joined: Wed Jun 09, 2010 11:48 pm
Location: west virginia university

Sponsor

Sponsor
 

Re: establishing identities with ^3 and ^4 in them  TOPIC_SOLVED

Postby Martingale on Thu Jun 10, 2010 2:09 am

bikeman wrote:i am asked two similar problems. my question is how it was done as the example in the book i am reading is useless in explaining.
the first question is:
(sin^3t+cos^3t)/(sint+cost)=1-sint cost
the example plays out to what i assume is factoring sint+cost out of it to look like (sint+cost)(sin^2t-sint cost+cos^2)/(sint+cost)

my question is, where did the "sin^2t-sint cost+cos^2" come from? when i factor it it doesnt look like that.

the next problem is (cos^4t-sin^4t)/(cos[2t]) how do i get rid of the ^4?


thanks for any help provided.




User avatar
Martingale
 
Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

Postby stapel_eliz on Thu Jun 10, 2010 2:13 pm

bikeman wrote: where did the "sin^2t-sint cost+cos^2" come from? when i factor it it doesnt look like that.

How did you factor? What did you get?

(To review how to factor differences of squares and sums and differences of cubes, try here). :wink:
User avatar
stapel_eliz
 
Posts: 1717
Joined: Mon Dec 08, 2008 4:22 pm

Re: establishing identities with ^3 and ^4 in them

Postby bikeman on Thu Jun 10, 2010 4:20 pm

I factored wrong.
i found that (cos^4t-sin^4t) is the same as saying (cos^2t+sin^2t)(cos^2t-sin^2t) one of which is a Pythagorean identity. the lower part of the problem, Cos(2t) is part of a series of identities which which cancels one half of the upper part of the equation. meaning you are left is 1 X1 which equals 1
bikeman
 
Posts: 2
Joined: Wed Jun 09, 2010 11:48 pm
Location: west virginia university


Return to Trigonometry