Question

csc(x) = (4√3)/(3) and cos(x)<0. Evaluate the function sin(x).
I know that sinθ = O/H and I know that H = 4√3 and A = 3. How do I find O?

Answer 1

you don't need to do that since csc(x) = 1/sin(x)

Answer 2

or sin(x) = 1/csc(x)

Answer 3

this is sin positive cos negative which is in the 2nd quadrant

but the easy way to do the problem is to recognise cosec(x) = 1/sin(x)

so sin(x) = 1/cosec(x)

\[\sin(x) = \frac{3}{4\sqrt{3}}\]

Answer 4

so since the 2nd quadrant the angle will be

180 - x

Answer 5

Thanks! That was really helpful!

Answer 6

good luck

Answer 7

Wait! Small problem... that's not one of my possible answers. Give me a second and I'll post them.

Answer 8

chances are you have to rationalize the denominator to get \[\Large \frac{3\sqrt{3}}{4}\]

Answer 9

That's still not one :(

Answer 10

alright post your possible answers please

Answer 11

oh wait, I made a typo lol...It should be \[\Large \frac{3\sqrt{3}}{12}\]

Answer 12

which reduces to \[\Large \frac{\sqrt{3}}{4}\]

Answer 13

A. sin(x) = -(√13)/(4)
B. sin(x) = -(4√13)/(13)
C. sin(x) = (√3)/(4)
D. sin(x) = -(√39)/(13)
E. sin(x) = -(√39)/(3)

Answer 14

So choice C

Answer 15

Let me know if you need help rationalizing the denominator

Answer 16

Thanks! I will :)

Answer 17

Basically, to rationalize the denominator, you multiply both top and bottom of the fraction by sqrt(3). This will make \[\Large \frac{3}{4\sqrt{3}}\] turn into \[\Large \frac{3\sqrt{3}}{4\sqrt{3}\sqrt{3}}\] which becomes \[\Large \frac{3\sqrt{3}}{12}\]

After fully simplifying, we get \[\Large \frac{\sqrt{3}}{4}\]


So \[\Large \sin(x) = \frac{\sqrt{3}}{4}\]