# Single Trig Functions

• Jul 14th 2010, 07:35 PM
nuckers
Single Trig Functions
Write the following as a single trigonometric function

$\displaystyle 1/2sin12xcos12x$

1/2 is a half, and the x value is theta, i wasn't sure how to do it that way. The question i have is this supposed to be 12theta, or should it be 2theta. i'm not sure how to do this.

Thanks
• Jul 14th 2010, 07:44 PM
mr fantastic
Quote:

Originally Posted by nuckers
Write the following as a single trigonometric function

$\displaystyle 1/2sin12xcos12x$

1/2 is a half, and the x value is theta, i wasn't sure how to do it that way. The question i have is this supposed to be 12theta, or should it be 2theta. i'm not sure how to do this.

Thanks

You're expected to know and use $\displaystyle \sin(2A) = 2 \sin (A) \cos (A)$.
• Jul 14th 2010, 07:45 PM
apcalculus
Let's assume it says 12x.

If we set u=12x, the expression becomes

$\displaystyle 1/2 sin u cos u$

The sine of a double angle formula says:

$\displaystyle 2 sin u cos u = sin (2u)$

Can you apply it here?

At the end, remember to write the expression in terms of the original variable x. Good luck!
• Jul 14th 2010, 07:46 PM
pickslides
$\displaystyle \frac{1}{2}\sin 12x \cos 12x$

$\displaystyle \frac{1}{4}\times 2\sin 12x \cos 12x$

Now apply $\displaystyle 2\sin u \cos u = \sin 2u$