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Inverse Functions (1 Viewer)

FDownes

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I'm not quite sure how to tackle this question. It asks;

a) Find the value of x such that sin-1x = cos-1x.

b) On the same diagram, sketch the graphs of y = sin-1x, y = cos-1x and y = sin-1x + cos-1x.

With this second part, I'm able to sketch the graphs of y = sin-1x and y = cos-1x, but I'm not sure how to sketch the third...
 
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wendus

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you can try doing it the dumb way and sort of just adding the values of y at each x value, like sketching normal inverse functions? otherwise i'm not too sure about part b.

and for part a do you mean sin^-1 x = cos^-1 x ?
 

lolokay

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sin-1x + cos-1x = pi/2, so the third graph of b will just be the line y = pi/2

and a) is just 1/sqrt2
if you didn't know that by inspection, your working could be as follows;
let x = sin@ = cos(pi/2 - @)
sin-1(sin@) = cos-1(cos(pi/2 - @))
@=pi/2-@
@=pi/4
sin pi/4 = 1/sqrt2
 
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