Inverse functions question -- Simultaneous equations (1 Viewer)

[blackops23]

Hi guys, quick question here:

Q. Solve for x and y

arcsinx + arccosy = pi/12 --- (1)

arcsiny - arccosx = 7pi/12 ---- (2)

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My working (someone please point out what is wrong with it)

(1) + (2)

arcsinx - arccosx + (arcsiny + arccosy) = 2pi/3
arcsinx - arccosx = 2pi/3 - pi/2 = pi/6

arcsinx - (pi/2 - arcsinx) = pi/6
2arcsinx - pi/2 = pi/6
2arcsinx = pi/6 + pi/2 = 2pi/3

arcsinx = pi/3

So x = sqrt(3)/2

Sub this in (1)

So: arcsin(sqrt(3)/2) + arccosy = pi/12

pi/3 + arccosy = pi/12
arccosy = pi/12 - pi/3 = -pi/4

so y = 1/sqrt(2)

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So now I had both values, x= sqrt(3)/2 and y=1/sqrt(2)

So i decided to sub the values in (1) to see if it works:

arcsinx + arccosy = pi/12
arcsin(sqrt(3)/2) + arccos(1/sqrt(2))
=pi/3 + pi/4
=7pi/12 --> not pi/12

subbing in (2)
arcsiny - arccosx = 7pi/12
arcsin(1/sqrt(2)) - arccos(sqrt(3)/2)
= pi/4 - pi/6
= pi/12 --> not 7pi/12


So what exactly did I do wrong?

Thanks, appreciate the help

 

[funnytomato]

arccosy = -pi/4

so y = 1/sqrt(2)

range of inverse cos?
where did u get that question?

 

[Hermes1]

i dont think this question is possible.

 

[blackops23]

range of inverse cos?
where did u get that question?

ahh ok thanks.... perhaps the question is wrong