Express arcsin x in terms of y

[CathyLou]

Hi.

Could someone please explain to me the following C3 level question? I would really appreciate any help as I am completely stuck at the moment.

Given that y = arccos x, -1 <= x <= 1 and 0 <= y <= pi,

(a) express arcsin x in terms of y.

I have written down that x = cos y but I do not know where to go from here. It says on the markscheme that:

x = sin (pi/2 - y) which leads to arcsin x = pi/2 - y

arcsinx = arcsin cos y

but I do not understand why this is the case. Could someone please help with this and part (b) of the question also?

(b) Hence evaluate arccos x + arcsin x. Give your answer in terms of pi.

Thank you.

Cathy

 

[mathboy]

Just draw a picture. We a dealing with a right triangle. Complementary angles add up to pi/2

 

[CathyLou]

Just draw a picture. We a dealing with a right triangle. Complementary angles add up to pi/2

Hi.

I have drawn a diagram but I still do not understand why x = sin (pi/2 - y). Could someone please explain?

Thank you for your help.

Cathy

 

[Dick]

cos(y)=sin(pi/2-y) from trig. So if x=cos(y), then also x=sin(pi/2-y). So arccos(x)=y means arcsin(x)=pi/2-y.

 

[CathyLou]

cos(y)=sin(pi/2-y) from trig. So if x=cos(y), then also x=sin(pi/2-y). So arccos(x)=y means arcsin(x)=pi/2-y.

Thank you for your help!

Cathy

 

[CathyLou]

Just draw a picture. We a dealing with a right triangle. Complementary angles add up to pi/2

Could someone please draw a diagram for me to compare mine to as I am not sure that I fully understand what it is meant to look like? Could you please label x and y?

Thank you.

Cathy

 

[Defennder]

Why don't you show your diagram here? Just upload a scan of it or something.

 

[PlasmaSphere]

hi. if your doing C3 for MEI sylabus this word document helps a lot, its a list of most of the equations they do not give you on any formula sheet. Only thing is that half of the equations are blank, and you have to fill them in, but its good practise. Its really helped me, I'm sitting C3 in a week or so.