# trigonometry

• Sep 11th 2006, 12:25 AM
sanya.batra
trigonometry
if A and B are acute angles and sinA=cosB,prove that A+B=90degrees
plz help me
• Sep 11th 2006, 01:27 AM
TD!
sin(a) = cos(b)
sin(a) = sin(pi/2-b)

a = pi/2-b <=> a+b = pi/2
OR
a = pi-(pi/2-b) <=> a = pi/2+b <=> a-b = pi/2

If a and b are positive and acute, the bold answer is the only one remaining.
• Sep 11th 2006, 01:36 AM
zanyzanny
Please see attached I hope this makes sense.
• Sep 11th 2006, 02:27 AM
Quick
Quote:

Originally Posted by zanyzanny
Please see attached I hope this makes sense.

It does but it's worded pretty poorly...
• Sep 11th 2006, 02:48 AM
zanyzanny
Quote:

Originally Posted by Quick
It does but it's worded pretty poorly...

I was trying to do it too quickly, sorry.
• Sep 11th 2006, 03:22 AM
CaptainBlack
Quote:

Originally Posted by zanyzanny
Please see attached I hope this makes sense.

Please try to avoid the use of proprietary file formats in attachments,
not everybody can read them in their native application which can result
in some unpleasant effects.

I would usually favour turning anything less than about 1 page into
a graphics format. I would recommend .png, but this site imposes a size
limit on .png files so in practice a high quality .jpg seems to work best.

RonL
• Sep 11th 2006, 04:27 AM
zanyzanny
Wow I have no idea what you just said or how you did that! :confused: :o
It looks good though.:)
Sorry I was just trying to be helpful. I don't have much idea about formats and stuff like that I am mostly interested in the maths :D
• Sep 11th 2006, 06:07 AM
Glaysher
Basically just do it in Paint. It gives you the option to save as a png file or a jpg file when you do Save As.
• Sep 11th 2006, 08:49 AM
Soroban
Hello, sanya.batra!

Here's a roundabout approach . . .

Quote:

Of A and B are acute angles and sin A = cos B,
prove that: A + B = 90°

We are given: .cos B .= .sin A . [1]

Square both sides: .cos²B .= .sin²A

Subtract from 1: .1 - cos²B .= .1 - sin²A

And we have: .sin²B .= .cos²A

Since A and B are acute: .sin B = cos A . [2]

Now consider: .sin(A + B)

. . . . . . . . . We have: .sin(A + B) .= .sin(A)·cos(B) + sin(B)·cos(A)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Substitute [1] and [2]: .sin(A + B) .= .sinA·sin(A) + cos(A)·cos(A)

Hence: .sin(A + B) .= .sin²A + cos²A . . sin(A + B) .= .1

Therefore: .A + B .= .90°

(Recall that A and B are both acute angles.)

• Sep 11th 2006, 08:58 AM
CaptainBlack
Quote:

Originally Posted by zanyzanny
Wow I have no idea what you just said or how you did that! :confused: :o
It looks good though.:)
Sorry I was just trying to be helpful. I don't have much idea about formats and stuff like that I am mostly interested in the maths :D

Produce the diagrams and text in any application you like.

Display them on the screen, then alt-PrintScreen will capture
the active window to the system clipboard. Open a graphics
application and paste, or paste-as-new to paste the clipboard
image into the application, crop to include only what you want
in the final image, then resize and save in favourite format.

Upload saved image file just like any other file and its done.

RonL