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anonymous
 5 years ago
what is the principal value of cos^1{cos 23pi/20}
anonymous
 5 years ago
what is the principal value of cos^1{cos 23pi/20}

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think, let me check with a calculator

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its an interesting method to solve , Ill do a quick picture now on paint and hopefully try to explain

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, not the best picture , but good enough . Now, first thing to notice is that the answer is not 23pi / 20 , because 23pi/20 is not in the range of cos^1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we must get the angle into the interval 0<x<pi

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and 23pi/20 is a bit more than pi

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey can you tell me what is meant by principal value?? i dont know if i get the idea u knw

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0however, the cos graph is symmetrical about the minimum points , that is cos(23pi /20) does equal the same value as cos (17pi /20) because they are both the same distance from the minimums

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0principal value just means , "your answer must be in the range 0<x<pi" pretty much only then does cos^1(cos(x)) = x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you really want to check your understanding then try \[\sin^{1} (\sin(\frac{23\pi}{20}))\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its a very similar idea

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0using translations of the graph , you get the angle into the range pi/2 to pi/2 ( because the range of sin^1 is pi/2 to pi/2 )

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then apply sin^1(sin(x)) = x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hmm.. i understand what you are saying. i would like to know how you got the value 17pi/20? i know its at a distance pi/4 from 23pi/4. i wanna know if there is some other way to work it out.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0there is other ways of working it our but I dont remember them at this point in time

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey is the prin. value for \sin^{1} (\sin(\frac{23\pi}{20})) 13 pi/20?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sin^{1} (\sin(\frac{23\pi}{20})) \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0draw a picture of a sin graph this time

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0my picture is not good, but you get the idea

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.023pi / 20 , is a bit more than pi , yes?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now, we need to get the angle 23pi/20 into the range pi/2 <= <= pi/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0isnt it at a distance pi/2 from it?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now, I know the graph of sin is symmetric about pi/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so if I find the distance between 23pi/20 and pi/2 , then this is the distance I must go to the left and I will still have the equivalent value of the function

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now, the distance between pi/2 and 23pi/ 20 = (23/20  1/2) pi = 13pi/20

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this means that if I go 13pi/20 units left from pi/2 , then I would be at a point that is a reflection in the line x=pi/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ie sin(23pi / 20 ) = sin ( pi/2  13pi/20 ) = sin ( 3pi/20 )

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now, since the angle of the sin function is in the range of the invese sin function

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can apply sin^1(sin(x) ) = x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so our answer is 3pi/20

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh..i understand now. thankyou so much=)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which can be checked on the calculator , put cal in radian mode , type in " sin^1(sin(23pi /20) )"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0with the brackets, and you will get something like 0.47 .... which is equal to 3pi/20
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