The solution is $-\frac16\pi$, ns don"t understand why?
If i pull up $-\frac16\pi$ top top a unit circle device (in this case on cannes Academy). The $y$ (the sine) value on the exact same angle $-\frac16\pi$ is $-\frac12$. I check out that the $x$ worth (the cosine) top top unit one of $-\frac16\pi$ is $\frac\sqrt32$.
Tan is opposite side / adjacent side, or in the unit circle"s instance sine/cosine. Which says to me the the tan of $-\frac16\pi$ is $-(1/2)/(\sqrt3/2)$ which equals $-1/\sqrt3$ no $-\frac16\pi$.
You are watching: Arctan(-sqrt(3))
Any insight would be great!
trigonometry
re-publishing
mention
monitor
edited Dec 8 "11 in ~ 0:19
André Nicolas
485k4343 yellow badges505505 silver- badges931931 bronze title
asked Dec 7 "11 at 23:55
drcdrc
22722 silver badges77 bronze title
$\endgroup$
9
| display 4 much more comments
2 answers 2
energetic earliest Votes
6
$\begingroup$
Maybe you"re just lacking the reality that $1/\sqrt3$ is the very same as $\sqrt3/3$. You acquire that by rationalizing the denominator:
$$\frac1\sqrt3 = \frac1\cdot\sqrt3\sqrt3\sqrt3 = \frac\sqrt33.$$
re-publishing
cite
monitor
reply Dec 8 "11 in ~ 0:13
Michael HardyMichael durable
1
$\endgroup$
1
add a comment |
1
$\begingroup$
Maybe you"re simply messing with the concept of inverse function... Remember:
$\arctan x=y$ if and only if $\tan y =x$ and $y\in >-\pi/2,\pi/2<$.
Now, you have uncovered $\tan (-\pi/6) =-1/\sqrt3=-\sqrt3/3$ and you additionally have $-\pi/6 \in >-\pi/2, \pi/2<$, for this reason previous declare applies and also it returns $\arctan (-\sqrt3/3)=-\pi/6$ together claimed.
re-publishing
mention
follow
edited Mar 5 "12 at 19:37
answered Dec 8 "11 at 0:28
PacciuPacciu
5,94811 yellow badge1515 silver- badges3838 bronze badges
$\endgroup$
5
include a comment |
your Answer
Thanks because that contributing an answer to 4476mountvernon.comematics stack Exchange!
Please be certain to answer the question. Provide details and share your research!But avoid …
Asking for help, clarification, or responding to other answers.Making statements based upon opinion; ago them up with references or an individual experience.Use 4476mountvernon.comJax to style equations. 4476mountvernon.comJax reference.
To learn more, see our tips on writing great answers.
See more: How Many Friends Can You Have On Pokemon Go Friend List Limit To 400
Draft saved
Draft discarded
Sign up or log in in
authorize up utilizing Google
authorize up making use of Facebook
sign up utilizing Email and also Password
submit
Post as a guest
name
email Required, but never shown
Post as a guest
name
Required, but never shown
article Your price Discard
By clicking “Post her Answer”, you agree to our terms of service, privacy policy and also cookie plan
Not the answer you're feather for? Browse other questions tagged trigonometry or ask your own question.
Featured on Meta
associated
8
Intuition because that graphing Sine/Cosine
2
Intuition around why domain the x that arcsine and also arccosine is <-1;1> for "real result" & domain for arctangent is all real numbers
0
discover the precise values without a calculator: (a) $\tan \frac11\pi 6$ (b) $\sec \frac-3\pi4$ (c) $\cot \frac-5 \pi3$
4
I gained a question around trig top top the unit circle
1
Deriving height(time) for a ferris wheel passenger?
1
The ratio of the political parties of a triangle offers us the edge of a line?
3
can I discover the size of the next of a triangle there is no a calculator?
1
If $\sinx=t, \quad x\in(\frac3\pi2,2\pi),$ what is $\tanx?$
1
What link do the hyperbolic trig functions have come the yes, really trig functions?
2
Discrepancy in assessing an integral $\int(\sqrt\tan x + \sqrt\cot x)dx$.
hot Network questions an ext hot questions
question feed
subscribe to RSS
question feed To subscribe to this RSS feed, copy and paste this URL into your RSS reader.
4476mountvernon.comematics
company
ridge Exchange Network
site design / logo © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.8.40416
4476mountvernon.comematics stack Exchange works finest with JavaScript permitted
her privacy
By clicking “Accept all cookies”, you agree ridge Exchange deserve to store cookies on your an equipment and disclose information in accordance v our Cookie Policy.