# Math Help - trignometric simplify

1. ## 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!!

2. btw how do you make the pi symbol on here??j

3. Hello,

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)

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

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

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

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

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

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

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

btw how do you make the pi symbol on here??j
$$\pi$$

4. thank you! most of that made sense to me, but what didnt wasnt your fault!

5. 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