Inverse Functions (1 Viewer)

[FDownes]

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...

 

[wendus]

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]

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