Expert: Sherman D. - 11/7/2004

Question
1.)  1/(cscx)(sec^2x) = ?

a.)1/(sinx)(cos^2x)
b.)sinx - sin^3x
c.)1/(sinx)(1+tan^2x)
d.)sinx - (1/1+tan^2x)
e.)1+tan^3x


2.)  solve the equation. find exact solutions when possible and approximate ones otherwise: cos 2x = cos x


I sincerely would like help on these questions because I'm struggling greatly on how to do them and any help would be much appreciated. Thanks a lot.


Answer
if by this you mean

1.)
1/((cscx)((secx)^2))) =
(1/(cscx)) * (1/((secx)^2))
(1/(1/sinx)) * (1/(1/((cosx)^2))))
((1/1)/(1/sinx)) * ((1/1)/(1/((cosx)^2)))
((1/1)*((sinx)/1)) * ((1/1)*((cosx)^2)/1)))
(sinx) * (cosx)^2
(cosx)^2 = 1 - (sinx)^2
so this gives you
(sinx)(1 - sinx^2)
work that out, and it gives you
sinx - (sinx)^3

so the answer is b.) sinx - (sinx)^3

by the way, if you go to Start, Programs, Accessories, System Tools, Character Map. You could type your problem as

1/((cscx)(sec²x)) and your answer as sinx - sin³x so that i don't get confused, because at first i thought it was
sec(2x) and sin(3x), but i decided to take it as raise to, because i figure thats what it was suppose to be.

Info can be found at http://www.oakroadsystems.com/twt/sixfunc.htm
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2.)
cos(2x) = cos(x)

going from 0 to 360 going by 60s
cos(x) =
cos(0) = 0
cos(60) = .5
cos(120) = -.5
cos(180) = -1
cos(240) = -.5
cos(300) = .5
cos(360) = 1

cos(2x) =
cos(2(0)) = 0
cos(2(60)) = -.5
cos(2(120)) = -.5
cos(2(180)) = 1
cos(2(240)) = -.5
cos(2(300)) = -.5
cos(2(360)) = 1

so i believe the answers are 0, 120, 240, 360
so in short, the answer is 120(k - 1), where k is the nth term.

I went to quickmath.com and it give me 0, -120, 120 as the answers.