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Evaluation trig functions

  • Thread starter Nyasha
  • Start date
127
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1. Homework Statement
[tex]cos(ArcSec(-\sqrt2+\frac{\pi}{4})[/tex]



3. The Attempt at a Solution

[tex]cos(ArcSec(-\sqrt2+\frac{\sqrt2}{2})[/tex]

In order to solve this problem how do l deal with the [tex]\frac{\pi}{4}[/tex]. Is it correct to substitute [tex]\frac{\pi}{4}[/tex] with [tex]\frac{\sqrt2}{2}[/tex]
 
316
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Hi Nyasha!

Why do you think that [tex]\frac{\pi}{4}\approx .785[/tex] is the same as [tex]\frac{\sqrt{2}}{2}\approx .707[/tex]?

You can however simplify cos(arcsec(...)).
 
127
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Hi Nyasha!

Why do you think that [tex]\frac{\pi}{4}\approx .785[/tex] is the same as [tex]\frac{\sqrt{2}}{2}\approx .707[/tex]?

You can however simplify cos(arcsec(...)).

So is this correct:


[tex]
cos(ArcSec(-\sqrt2+(0.785))
[/tex]
 
316
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Well, you don't need to use decimal notation (and probably should not in this case), I was just trying to demonstrate that the two numbers are not the same.

What I was hinting at before: sec(x)=1/cos(x), so arcsec(x)=arccos(1/x) and also cos(arccos(x))=x by definition. Use this to simplify your expression.
 
127
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Well, you don't need to use decimal notation (and probably should not in this case), I was just trying to demonstrate that the two numbers are not the same.

What I was hinting at before: sec(x)=1/cos(x), so arcsec(x)=arccos(1/x) and also cos(arccos(x))=x by definition. Use this to simplify your expression.


I can evaluate this thing without the [tex] \frac{\pi}{4} [/tex] by the assistance of of the principal range of arcsec and a diagram. I just am just getting confused with the [tex]\frac{\pi}{4}[/tex].
 
127
0
Well, you don't need to use decimal notation (and probably should not in this case), I was just trying to demonstrate that the two numbers are not the same.

What I was hinting at before: sec(x)=1/cos(x), so arcsec(x)=arccos(1/x) and also cos(arccos(x))=x by definition. Use this to simplify your expression.
Thanks, l have solved the question.

[itex]\text{Using pricinpal values: }\:\text{arcsec}\left(\text{-}\sqrt{2}\right) \:=\:\frac{3\pi}{4}[/itex]


And then add the [itex]\frac{3\pi}{4}[/itex] to the[itex]\frac{\pi}{4}[/itex]
 
316
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So it really was [tex]\text{cos}(\text{arcsec}(-\sqrt{2})+\frac{\pi}{4})[/tex]? Otherwise, it is not correct.
 
127
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So it really was [tex]\text{cos}(\text{arcsec}(-\sqrt{2})+\frac{\pi}{4})[/tex]? Otherwise, it is not correct.

Yes it was :


[tex]\{cos}(\text{arcsec}(-\sqrt{2})+\frac{\pi}{4})[/tex]



It seemed as if l had copied the thing wrongly.


However,it seems as if l have solved it.
 

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