# trignometric simplify

• May 6th 2008, 12:08 PM
antz215
trignometric simplify
Find: sin(arccos(3/5))

Find the exact value of csc105 degrees

Simplify: sin (x+y) - sin(x-y)

Prove that: sin2x/cotx = 1-cos2x

Find the exact value of sin(x+ pi/3)

I know thats a lot but any help would be amazing!!! I'm awful at this!!
• May 6th 2008, 01:09 PM
antz215
btw how do you make the pi symbol on here??j
• May 6th 2008, 01:16 PM
Moo
Hello,

Quote:

Originally Posted by antz215
Find: sin(arccos(3/5))

$\sin(\arccos(3/5))=\pm \sqrt{1-(3/5)^2}$ (see where arccos 3/5 lies and conclude about the sign of the sine)

Quote:

Find the exact value of csc105 degrees
Dunno.. have to find out what csc is...

Quote:

Simplify: sin (x+y) - sin(x-y)
$\sin(x+y)=\sin(x)\cos(y)+\cos(x)\sin(y)$

$\sin(x-y)=\sin(x)\cos(-y)+\cos(x)\sin(-y)$

Quote:

Prove that: sin2x/cotx = 1-cos2x
$\cot x=\frac{\cos x}{\sin x}$

$\sin 2x=2 \cos x \sin x$

$\Longrightarrow \frac{\sin 2x}{cot x}=2 \sin^2(x)=\dots$

Quote:

Find the exact value of sin(x+ pi/3)
Use the formula $\sin(x+y)=\sin(x)\cos(y)+\cos(x)\sin(y)$

Quote:

btw how do you make the pi symbol on here??j
$$\pi$$ (Wink)
• May 6th 2008, 01:28 PM
antz215
thank you! most of that made sense to me, but what didnt wasnt your fault!
• May 6th 2008, 01:31 PM
Moo
Quote:

Originally Posted by antz215
thank you! most of that made sense to me, but what didnt wasnt your fault!

I can try to explain, as far as my knowledge allows me :)