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anonymous
 one year ago
What is this TRIG identity called. see attachment.
anonymous
 one year ago
What is this TRIG identity called. see attachment.

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure if there is a specific name for this identity

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how would I explain it though

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0I guess you could say "composition of a trig function and another inverse" ? I'm not sure

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0oh you want to know how they got that identity?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0here let me give you an example

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0tan(arccos(x)) let theta = arccos(x) so cos(theta) = x = x/1 agreed?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\tan(\cos^1(1/2)\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0so we can create this right triangle dw:1438215201249:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438215224912:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0cos(theta) = x/1 cosine deals with adjacent over hypotenuse

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0so we can add these labels dw:1438215259342:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0what is the missing side equal to (in terms of x) ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0it will be the square root of that

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438215360088:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 how do we gate the base of absolute value of x

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0tan(arccos(x)) turns into tan(theta) this is because I let theta = arccos(x) calculating tan(theta) gives \[\Large \frac{\text{opposite}}{\text{adjacent}} = \frac{\sqrt{1x^2}}{x}\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0for some reason, and I don't know why, they made the denominator be x instead of just x. My guess is that they wanted to force tan(arccos(x)) to be positive. However, tan(arccos(x)) is only positive when x is positive

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.0So it should be \[\Large \tan(\arccos(x)) = \frac{\sqrt{1x^2}}{x}\]
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