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trigonometry exam question watch

1. I'm doing part a, and I dont know where to start. can someone explain this question to me please? thanks

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2. y=arccosx.
cosy=x
siny=??
y=arccosx.
cosy=x
siny=??
4. (Original post by Maths&physics)
I'm doing part i, and I dont know where to start. can someone explain this question to me please? thanks

This was one of the worst answered Edexcel pure questions of all time by the way. Nasty question.
6. (Original post by Notnek)
This was one of the worst answered Edexcel pure questions of all time by the way. Nasty question.
yeah, I dont get it.

I see that cos y = x

then I dont know where to go from there?
7. (Original post by Maths&physics)
yeah, I dont get it.

I see that cos y = x

then I dont know where to go from there?
Do you know an identity that links cos and sin (not cos^2 and sin^2)? It’s a less used identity but can be seen by observing that sin/cos are translations of each other.
8. (Original post by Notnek)
Do you know an identity that links cos and sin (not cos^2 and sin^2)? It’s a less used identity but can be seen by observing that sin/cos are translations of each other.
no, I dont know, what is it?
9. (Original post by Maths&physics)
yeah, I dont get it.

I see that cos y = x

then I dont know where to go from there?
Well tbh just arcsin both sides and say done
10. For part b, should be Pi/2 (90 degrees)
11. try out some numbers...

π/3 = arccos {1/2} .... π/3 is the angle whose cos is 1/2

π/6 = arcsin {1/2}.......π/6 is the angle whose sin is 1/2

if the angles are acute you can see that they add up to π/2
12. (Original post by Notnek)
Do you know an identity that links cos and sin (not cos^2 and sin^2)? It’s a less used identity but can be seen by observing that sin/cos are translations of each other.
cos(x) = sin(x+pi/2)

I dont know if thats an identity but looking at both graphs simultaneously, thats what I see.
13. (Original post by RDKGames)
Well tbh just arcsin both sides and say done
thats not the right answer though
14. (Original post by Maths&physics)
thats not the right answer though
It's in terms of so technically you answer their question.

Though if you really want to play by the rules then you need to use the identity you stated following on from , except you want to use instead.
15. Could you just do this using graphical method? If they are saying "express arcsinx in terms of y" this implies we need to do something to y=arccosx such that its the same as arcsinx. So if you do -arccosx +pi/2 you see that after this transformation the arccosx graph is exactly the same as arcsinx graph, therefore arcsinx=-y+pi/2, so for the next part we just combine all of this and do y+-y+pi/2 which is just pi/2
16. (Original post by RDKGames)
Well tbh just arcsin both sides and say done
Doesn’t help much with part b though
17. (Original post by Notnek)
Do you know an identity that links cos and sin (not cos^2 and sin^2)? It’s a less used identity but can be seen by observing that sin/cos are translations of each other.
so, I'm looking at the arcs and arcsin graphs.

for arcsin to = arcos (y), it must reflect in the y axis (-y) and go up pi/2?

which means arcsinx = pi/2 - y ????

is that right way of thinking and doing it?
18. (Original post by Maths&physics)
so, I'm looking at the arcs and arcsin graphs.

for arcsin to = arcos (y), it must reflect in the y axis (-y) and go up pi/2?

which means arcsinx = pi/2 - y ????

is that right way of thinking and doing it?
That's correct. The more standard approach would be to consider sin/cos. The identities you need are

This is why e.g. sin(60) = cos(30) and cos(80) = sin(10) in other words the sin/cos angles add up to 90 or radians. You need to know these identities for the exam (although they're used rarely).

Back to the question:

Can you finish it off to find in terms of ?
19. (Original post by Notnek)
That's correct. The more standard approach would be to consider sin/cos. The identities you need are

This is why e.g. sin(60) = cos(30) and cos(80) = sin(10) in other words the sin/cos angles add up to 90 or radians. You need to know these identities for the exam (although they're used rarely).

Back to the question:

Can you finish it off to find in terms of ?
thanks!! no i can't, i don't understand how you got the answer. what did you do?
20. (Original post by Maths&physics)
thanks!! no i can't, i don't understand how you got the answer. what did you do?
E.g.

becomes

You can do a similar thing here.

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