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bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0\[\cos(\arcsin(\frac{ \sqrt{3} }{ 2 }))\]

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sin^{1}\frac{ \sqrt{3} }{ 2 }\]This is an angle measurement. Like if you had \[\sin \theta = \frac{ \sqrt{3} }{ 2 }\]You would find theta by taking the inverse. Use your knowledge of the unit circle to find the value of the y coordinate (sine) at sqrt(3)/2. Then once you have this, you can find cos of whatever it was

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0okay so arc sin is actually sin^1

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1Ya they are used interchangeably.

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0so it's sin of 30 degrees?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2\[\text{ Let } u=\arcsin(\frac{\sqrt{3}}{2})\] => \[ \sin(u)=\frac{\sqrt{3}}{2}\] sin( )=opp/hyp So we can do this: dw:1352310919231:dw Use Pythagorean thm to find the adjacent side to u. Then you can find cos(u) which is the same as what your question is asking since we \[\text{ let } u=\arcsin(\frac{\sqrt{3}}{2})\] \[\cos(u)=\cos(\arcsin(\frac{\sqrt{3}}{2}))=\frac{\text{ adjacent side to u}}{hyp}\]

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0right so it's just root 3 over 2

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2Nope sin(u) is that what is cos(u)?

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0or it's at 60 degrees and 120

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1Based on the unit circle, sqrt(3)/2 (the y value) is at 60 deg. So it would be cos 60deg

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1right it is also at 120. good catch

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0so i write it as cos(60) ??

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0so my answer should be 1/2 and 1/2?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2but arcsin( ) only has range between 90 and 90.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2So you will only have one answer.

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1Explain that plx @myininaya . I don't remember that.

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0i thought that had to be specified

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1http://en.wikipedia.org/wiki/Inverse_trigonometric_functions He's right. The only answer would be 1/2

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2In order to make sin( ) one to one, we must restrict the domain of sin( ) in order to do this. We chose the restriction [90 degrees, 90 degrees] So now that are inverse for sin( ) exists, we call it arcsin( ). And arcsin( ) only has range [90 degrees, 90 degrees]

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0i can only do this type of problem if it's one to one?

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0so if i wanted to do sec(arctan(2)) i do the same thing?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2I like making a pretty right triangle. :)

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2\[\text{ Letting } u=\arctan(2) \] => tan(u)=2 tan(u)=2/1 tan(u)=opp/adj We let opp side of u be 2 We let adj side of u be 1 Let the labeling begin.dw:1352311632755:dw Now find the hyp by using the Pythagorean thm.

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2After that, find sec(u) and you are done.

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0there is no hypotnus tho :s

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2Yes there is. You find it by using the Pythagorean thm.

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0square root of 5 is the hyp.

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0okay so now i take sec(squareroot 5)

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0and do i restrict my tan?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1352311961504:dw

ChmE
 2 years ago
Best ResponseYou've already chosen the best response.1Study her method because it was way easier than my explanation.

bmelyk
 2 years ago
Best ResponseYou've already chosen the best response.0and i state my domain and range for just sec right?

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2No it was just looking for sec(arctan(2)) which is just \[\sqrt{5}\]
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