Question

Let sin x denote the sine function.....

Rest of problem drawn inside!! :)

Answer 1

I don't really get this... could you please explain it step by step? thank s so much!!

Answer 2

Is your question whether
$$
\cfrac{0.25\times \sin4t}{4}
$$
Is equivalent to
A. \(\sin4\)
B. \(\sin t\)
C. \(\sin\)
D. \(\cfrac{\sin 4}{4}\)
E. None of the above
?

Answer 3

Note that
$$
\sin 2t=2\cos t\sin t\\
\sin 4t=2\cos2t\sin2t
$$
So
$$
\cfrac{0.25\times \sin4t}{4}\\
=\cfrac{1/4}{4}\times2\cos2t\sin2t\\
=\cfrac{1}{8}\times2\cos2t\sin2t\\
=\cfrac{\cos2t\sin2t}{4}\\
$$

Answer 4

Correction,
$$
\cfrac{0.25\times \sin4t}{4}\\
=\cfrac{1/4}{4}\times2\cos2t\sin2t\\
=\cfrac{1}{16}\times2\cos2t\sin2t\\
=\cfrac{\cos2t\sin2t}{8}\\
$$

Answer 5

yes, that is my problem :)

okay so what do you do from there? :)

Answer 6

The answer is above and doesn't match any of your options, A-D.

Answer 7

ohh okay i see.. so it's just E then...

so if i ever have problems like that, i'm plugging in the sin value and solving? like you did above?

Answer 8

Not always, sometimes it's easier. For example, notice that your original problem has a \(t\) in formula. 3 of the answers DON'T have a t, so you can exclude them. Be careful, though because sometimes the variable (like t here) will cancel in the denominator.

Best to try to use trig identities. There really aren't a lot of them and you don't necessarily need to remember them all, but know that they are there and have them handy. It does help to remember some of the easier ones.

Try to simply answers such that the argument, like the \(t\) in \(\sin t\) is as simple as possible. We had 4t here, 2t is simpler, t is even simpler.

Look at some of the trig problems people are solving here and jump in and try to help, you'll learn so much.

Good Luck!

Answer 9

okay, awesome!! thank you so much!! :)