# Math Help - Lotta trig work to do tonight

1. ## Lotta trig work to do tonight

Yay! I wish I'd found this forum earlier. I'll definitely be back later to offer whatever help I can, but for tonight I have alot of trig work to get through, so any help from any other mathematical night owls (or antipods) will be really, really appreciated! I won't even ask for answers handed on a silver platter, I just need help getting through most of them.

For starters:
3 - 6sin^2 (4x)

So far I've got:

3(1 - 2sin^2(4x))
double angle formula: (cos(2(x)) = 1 - 2sin^2(x) )
3(cos(2(4x)))
=3cos(8x)

Does everything I've done there so far check out?

The problem requests "write each expression as a single function of a single angle". That says to me that I need to get the 3 onto the other side of the trig function, but I can't find any trig identities or formulas that tell me how to do that. Am I wrong in thinking that and the expression is as simplified as it's going to get, or is there some other identity or formula that will take it further?

(also, if anyone can tell me how to type exponents, that'd come in handy. I know how to do them in Word, but the same keypad function doesn't work most places online. It's not a big deal, since ^2 usually gets the message across)

2. Originally Posted by Poaceaejumper
Yay! I wish I'd found this forum earlier. I'll definitely be back later to offer whatever help I can, but for tonight I have alot of trig work to get through, so any help from any other mathematical night owls (or antipods) will be really, really appreciated! I won't even ask for answers handed on a silver platter, I just need help getting through most of them.

For starters:
3 - 6sin^2 (4x)

So far I've got:

3(1 - 2sin^2(4x))
double angle formula: (cos(2(x)) = 1 - 2sin^2(x) )
3(cos(2(4x)))
=3cos(8x)

Does everything I've done there so far check out?

The problem requests "write each expression as a single function of a single angle". That says to me that I need to get the 3 onto the other side of the trig function, but I can't find any trig identities or formulas that tell me how to do that. Am I wrong in thinking that and the expression is as simplified as it's going to get, or is there some other identity or formula that will take it further?

(also, if anyone can tell me how to type exponents, that'd come in handy. I know how to do them in Word, but the same keypad function doesn't work most places online. It's not a big deal, since ^2 usually gets the message across)
what you did is fine.

^2 does get the message across, but for typing "pretty" math, use LaTex

3. "Find all solutions (algebraically) of the equation in the interval [0, 2pi]"

tan^2 (2x) = 3

I'm burned out and blanking. Every identity I try just complicates it, or leads me in circles. Help

4. $\tan^22x=3\Rightarrow\tan 2x=\pm\sqrt{3}$

1) $\tan 2x=\sqrt{3}\Rightarrow 2x=\frac{\pi}{3}+k\pi\Rightarrow x=\frac{\pi}{6}+\frac{k\pi}{2}$
$k=0\Rightarrow x=\frac{\pi}{6}$
$k=1\Rightarrow x=\frac{2\pi}{3}$
$k=2\Rightarrow x=\frac{7\pi}{6}$
$k=3\Rightarrow x=\frac{5\pi}{3}$

2) $\tan 2x=-\sqrt{3}\Rightarrow 2x=-\frac{\pi}{3}+k\pi\Rightarrow x=-\frac{\pi}{6}+\frac{k\pi}{2}$
and so on...