This chapter is so confusing to me. Is there a simple way to go about this?

find a numerical value of one triganomic function of each x.

2 sin^2x = 3 cos^2x

1-sin^2x = 1/9

1+ tan^2x = sin^2x + 1/sec^2x

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- Jan 24th 2006, 11:30 AMmathAna1ys!5numerical value (trig)
This chapter is so confusing to me. Is there a simple way to go about this?

find a numerical value of one triganomic function of each x.

2 sin^2x = 3 cos^2x

1-sin^2x = 1/9

1+ tan^2x = sin^2x + 1/sec^2x - Jan 24th 2006, 11:57 AMThePerfectHacker
First one,

$\displaystyle 2\sin^2x=3\cos^2x$

Use identity $\displaystyle \cos^2x=1-\sin^2x$.

Thus,

$\displaystyle 2\sin^2x=3(1-\sin^2x)$

Thus, open parantheses,

$\displaystyle 2\sin^2x=3-3\sin^2x$

Thus,

$\displaystyle 5\sin^2x=3$

Thus,

$\displaystyle \sin^2x=\frac{3}{5}=\frac{15}{25}$

Thus,

$\displaystyle \sin x=\pm\frac{\sqrt{15}}{5} \approx \pm.775$

Thus, all non-cotermial angles are, (use the arcsin)

$\displaystyle x\approx 51,129,231,309$ - Jan 24th 2006, 12:03 PMThePerfectHacker
Second one,

$\displaystyle 1-\sin^2x=\frac{1}{9}$

Use identity $\displaystyle 1-\sin^2x=\cos^2x$

Thus, $\displaystyle \cos^2x=\frac{1}{9}$

Thus,

$\displaystyle \cos x=\pm \frac{1}{3}$

Thus, all the non-coterminal angles, (use arccos)

$\displaystyle x\approx 71,109,251,289$ - Jan 24th 2006, 12:09 PMThePerfectHacker
Problem 3,

$\displaystyle 1+\tan^2x=\sin^2x+\frac{1}{\sec^2x}$

Use identity $\displaystyle \frac{1}{\sec x}=\cos x$

Thus,

$\displaystyle 1+\tan^2x=\sin^2x+\cos^2x$

Use identity $\displaystyle \sin^2x+\cos^2x=1$

Thus,

$\displaystyle 1+\tan^2x=1$

Thus,

$\displaystyle \tan^2x=0$

Thus,

$\displaystyle \tan x=0$

Thus, all the non-coterminal angles, (use arctan)

$\displaystyle x=0,180$.

Q.E.D. - Jan 24th 2006, 12:10 PMmathAna1ys!5
so more than one problem relating to the same topic counts as multiple posts?

- Jan 24th 2006, 12:26 PMThePerfectHacker
I saw that you made multiple posts on the topic of trigonometry. I do not think you want to "spam" the forum. I would allow it, but be careful and do not start asking the same question everywhere, because then we, the moderators, have to waste time deleting them. CaptainBlack already banned a person for 1 day for doing "spamming".

- Jan 24th 2006, 01:36 PMCaptainBlackQuote:

Originally Posted by**ThePerfectHacker**

fora, at most I may have deleted all but one.

The person in question posted exactly the same message 5 times (and may

have been still posting copies when I banned them), and the message was

not a question but publicity for their web site (admittedly mathematical).

As it is I have left one copy of their message online.

I must confess to being touchy about spam on message boards, and if I

have the ability to stop it I will. I have seen enough good sites ruined by

spam.

RonL