You are Here: Home >< Maths

# C3 Trig Q watch

1. 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
2. What didn't you understand?

Did you know ?

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).
3. 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
4. (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.

Let
5. 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?
6. (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?
7. yeah with that in mind , but I'll ask about it when we go back, thanks anyway
8. (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

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 1, 2013
Today on TSR

### Congratulations to Harry and Meghan!

But did you bother to watch?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams