Question

Find all solutions of the equation in the interval [0, 2pi). (sqrt3)csctheta+2 = 0. Write your answer in radians in terms of pi

Answer 1

\[\sqrt{3}\csc \theta+2=0\]

Answer 2

I rarely use csc or sec, and so would first translate to 1/sin

Answer 3

Okay so
\[\sqrt{3}(1/\sin \theta) + 2 = 0\]

Answer 4

now add -2 to both sides, then divide both sides by sqr(3)

Answer 5

you should get
\[ \frac{1}{\sin \theta}= - \frac{2}{\sqrt{3}} \]

Answer 6

now invert (i.e. "flip" ) both sides

Answer 7

Okay, got it! Sorry, was following along with you while writing it down on paper

Answer 8

Flip as in, turn upside down?

Answer 9

yes, as in making the left side sin theta instead of 1/sin theta
ditto for the right side.

Answer 10

\[\frac{ \sin \theta }{ 1 } = \frac{ -2 }{ \sqrt{3} }\]

Answer 11

yes, but most people would just write sin theta on the left side

Answer 12

oh, you have to flip the right side also

Answer 13

Oh, I forgot to flip the other side, sorry!

Answer 14

\[\sin \theta = -\frac{ \sqrt{3} }{ 2 }\]

Answer 15

usually, people memorize sin of certain angles: 0, 30, 45, 60 and 90 degrees
this is one of those angles.

Answer 16

*ignoring the sign, for the time being *

Answer 17

Is it 60? (ignoring the sign)

Answer 18

yes. now we need to find the actual angle
to get a general idea, we (maybe?) know that -sqr(3)/2 is about -.8 (roughly)
if we plot a sin curve