Question

Evaluate the limit as x goes to (9pi/4):
sin(x)/(8x)

Answer 1

I plugged in and came up with some wild answer - I'll redo - thanks!

Answer 2

Just plug in x.
sin(9pi/4)=sqrt(2)/2
8*9pi/4=18pi
sqrt(2)/36pi
or:
\[\frac{\sqrt{2}}{36 \pi}=\frac{1}{18 \pi \sqrt{2}}\].

Answer 3

http://www.wolframalpha.com/input/?i=limit+of+sin(x)%2F8x%2Cx%2C9pi%2F4

Answer 4

thanks malevolence! Did you get sin(9pi/4) from the unit circle?

Answer 5

Yes. You know that 2pi is the same as zero? So 8pi/4=2pi. So go one pi/4 further, that takes you to the first quadrant so its positive. (that's all the quadrant is important for)

Answer 6

yes

Answer 7

so, I have to have that memorized for my test I assume! :-)

Answer 8

thanks again fo r the explanation!

Answer 9

No problem. Just remember the first quadrant. Then after that, all you have to remember is the sign's for the quadrant. All of them are positive in the first, sine is positive in the second (the y-coordinate), tangent is positive in the 3rd (its sin(x)/cos(x) and both are negative [x and y coords]), then cosine is positive in the 4th quadrant (x coordinate).

Answer 10

oh of course! then the rest uses pythogaros,

Answer 11

is that correct?

Answer 12

Yup :)

Answer 13

sweet! thanks a ton!