Question

Which of the following are solutions to the equation sinx cos x = 1/4? There can be more than one.
PI/3 + nPI/2
PI/6 + nPI/2
PI/12 + nPI
5PI/12 + nPI

Answer 1

\[\large \sin x \cos x = \frac{1}{4}\]Multiplying both sides by 4 will give us:\[\large 4 \sin x \cos x = 1\]

Answer 2

This is another problem where we want to remember a trig identity, specifically, Sine Double Angle.
\[\large 2\sin x \cos x = \sin 2x\]

Answer 3

If we apply this to our problem, we have...
\[\large 4 \sin x \cos x = 1\]\[\large 2 \cdot 2\sin x \cos x = 1\]\[\large 2 \cdot \sin 2x = 1\]

Answer 4

\[\large \sin 2x = 1/2\]

Answer 5

We'll need to solve for 2X before we can solve for X.
Remember the reference angle for this one?
\[\large \sin \theta = 1/2\]
What values of theta give you a half? :D

Answer 6

um sin2x?

Answer 7

wait ...er 60?

Answer 8

Ummmmm I think it's attttttttttt 30 degrees actually :o
Since we're dealing with radians, we want the radian measure of 30 degrees. (pi/6)

BUT, that is the reference angle for 2x!
So now we want to solve for x.
\[\large 2x=\frac{\pi}{6}\]Dividing both sides by 2 gives us,\[\large x=\frac{\pi}{12}\]
If it's confusing, maybe go back over the stuff I posted :3 or ask questions.

Answer 9

so what are the answers if its pi/12? 0.o

Answer 10

@zepdrix

Answer 11

It's the option involving pi/12 :D

Answer 12

im pretty sure there's only one of those XD

Answer 13

are you sure?

Answer 14

well you are wrong @zepdrix it was c and d .....so ..yah

Answer 15

oh i didn't realize you could choose 2 of the 4... wish you woulda mentioned that :\ i woulda paid more attention.. soz