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August 19, 2019, 01:36:20 am

Author Topic: 3U Maths Question Thread  (Read 538944 times)  Share 

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RuiAce

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Re: 3U Maths Question Thread
« Reply #4185 on: August 09, 2019, 07:43:37 pm »
+1
yes, but cos inverse 1 also equals 2pi, so how do you know which one to use?

for the second one, my question was how do you then isolate x from your last line?
This red bit is not true.
\[ \text{The function }f(x) = \cos^{-1}x\text{ has range }0\leq y \leq \pi.\\ \text{The value it returns }\textbf{must}\text{ be a value associated with the first or second quadrant.} \]

Note that the \(x\) can also be isolated in the second equation by brute force: \(\displaystyle2x = 2n\pi \pm \frac\pi2 - \frac\pi4 \implies \boxed{x=n\pi \pm \frac\pi4 - \frac\pi8}\). Although I would favour fun_jirachi's answer over this notation.

spnmox

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Re: 3U Maths Question Thread
« Reply #4186 on: August 09, 2019, 08:56:51 pm »
0

So as you can see it doesn't actually matter if you we use 0 or 2pi since 2n and 2n+1 are both integers. Just looks nicer and cleaner to use 0 (EDIT: also it's correct unlike using 2pi [refer to next post :)]).

To isolate x:


thank you :) how did you combine the two answers?

spnmox

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Re: 3U Maths Question Thread
« Reply #4187 on: August 09, 2019, 08:57:13 pm »
0
This red bit is not true.
\[ \text{The function }f(x) = \cos^{-1}x\text{ has range }0\leq y \leq \pi.\\ \text{The value it returns }\textbf{must}\text{ be a value associated with the first or second quadrant.} \]

Note that the \(x\) can also be isolated in the second equation by brute force: \(\displaystyle2x = 2n\pi \pm \frac\pi2 - \frac\pi4 \implies \boxed{x=n\pi \pm \frac\pi4 - \frac\pi8}\). Although I would favour fun_jirachi's answer over this notation.

thank you, that clears it up!!