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C3 Trig Q

Hi guys, would anyone know how to answer this question:

Given that:

y = arccos x

-1<(or equal to) x < (or equal to) 1

0 < (or equal to) y < (or equal to) pi


a) express arcsin x in terms of y


So far I have x = cos y, but the mark scheme then writes:

x = sin(pi/2 -y)

arcsin x = pi/2 -y

Any help'd be great
What didn't you understand?

Did you know cos⁡y=sin⁡(π2−y)\cos y = \sin (\frac{\pi}{2}-y) ?

The graphs of y=sin x and y=cos x are translations of each other.

Draw a right angled triangle and call one angle y, one pi/2 and the other (pi/2 - y). Try to see why this identity is true.

Alternatively use the expansion of sin(A - B).
(edited 11 years ago)
Reply 2
Avatar for sinkersub
sinkersub
OP
I understand that cos x = sin(x + pi/2)

because the cos graph is the sine graph moved pi/2 to the left (I think), but I can't see how sin(pi/2 - y) relates in the same way sorry
Original post by sinkersub
I understand that cos x = sin(x + pi/2)

because the cos graph is the sine graph moved pi/2 to the left (I think), but I can't see how sin(pi/2 - y) relates in the same way sorry


Well I have shown you two methods but here's a third.

sin⁡θ=sin⁡(π−θ)\sin \theta =\sin(\pi - \theta)

Let θ=x+π2\theta = x + \frac{\pi}{2}
Reply 4
Avatar for sinkersub
sinkersub
OP
I think I got it, but roughly,

Is it ok to look at the graphs or arccos and arcsin individually, and the fact that arcsin up by pi/2 and flipped in the y axis gives the same translation?
Original post by sinkersub
I think I got it, but roughly,

Is it ok to look at the graphs or arccos and arcsin individually, and the fact that arcsin up by pi/2 and flipped in the y axis gives the same translation?


That's fine but you must use the proper language of transformations. Up? Flipped?
Reply 6
Avatar for sinkersub
sinkersub
OP
yeah with that in mind , but I'll ask about it when we go back, thanks anyway
(edited 11 years ago)
Reply 7
Avatar for TenOfThem
TenOfThem
18
Original post by sinkersub
I think I got it, but roughly,

Is it ok to look at the graphs or arccos and arcsin individually, and the fact that arcsin up by pi/2 and flipped in the y axis gives the same translation?


This is a 1 mark question

You are expected to know that arcsinx + arccosx = pi/2

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