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
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)
$\displaystyle x\approx 51,129,231,309$
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)
$\displaystyle x\approx 71,109,251,289$
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.
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".
I would not have banned them for posting the same question to multipleOriginally 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