Question

if 0 degrees < x<360 degrees, solve the equation sin x= -sqrt 3/2

Answer 1

what?

Answer 2

that makes no sense?

Answer 3

http://i.stack.imgur.com/r8uHr.gif

Answer 4

sorry made a mistake
4pi/3

Answer 5

but yea use the unit circle

Answer 6

sinx=sin(-π/3) ,(0,2π)

x=2kπ - (π/3) or x=2kπ + π -(π/3)
x=2kπ + (2π/3) k∈Z


0<x<2π
0<2kπ - (π/3)<2π or 0<2kπ + (2π/3)<2π
solve the above inequalities for k (k is an integer)

Answer 7

so the answer is 150 degrees and 300 degrees?

Answer 8

\(\bf sin(x)= -\sqrt{\frac{3}{2}}\quad \textit{taking }sin^{-1}\textit{ to both sides}\\ \quad \\
sin^{-1}[sin(x)]= sin^{-1}\left(-\sqrt{\frac{3}{2}}\right)\implies x= sin^{-1}\left(-\sqrt{\frac{3}{2}}\right)\)

Answer 9

\(\bf \textit{recall that }sin^{-1}[sin(\theta)]=\theta\)

Answer 10

\(\bf sin^{-1}\left(-\sqrt{\frac{3}{2}}\right)\implies \textit{the angle(s) whose sine is }-\sqrt{\frac{3}{2}}\)

Answer 11

so check your unit circle

Answer 12

okay so then its 120 and 240? in degrees

Answer 13

240 is in the 3rd quadrant, sine is negative there, yes
120 is in the 2nd quadrant, sine is positive there, no dice

Answer 14

notice, is a negative \(\Large -\sqrt{\frac{3}{2}}\)

Answer 15

soo then it has to be 300 then

Answer 16

yeap

Answer 17

thank you

Answer 18

lemme recheck something

Answer 19

ok

Answer 20

ohh... I see.. nevermind... you meant ... to write I gather \(\bf sin(x)= -\cfrac{\sqrt{3}}{2}\quad \textit{taking }sin^{-1}\textit{ to both sides}\\ \quad \\
sin^{-1}[sin(x)]= sin^{-1}\left(-\cfrac{\sqrt{3}}{2}\right)\implies x= sin^{-1}\left(-\cfrac{\sqrt{3}}{2}\right)\\ \quad \\
x=
\begin{cases}
240^o\\
\bf 300^o
\end{cases}\)

just making the distinction, that \(\bf -\cfrac{\sqrt{3}}{2}\ne -\sqrt{\cfrac{3}{2}}\)

Answer 21

actually the signs "<" are suppose to be greater that or equal to for both so wold it still be 240 and 300?

Answer 22

0 < x < 360 just means

0 < x <--- "x" is greater than 0
x < 360 <---- "x" is lesser than 360

well, 240 is greater than 0 and less than 360
300 is also greater than 0 and less than 360

Answer 23

they're not BELOW 0 or equals it, they're not ABOVE 360 or equals it

Answer 24

240 degrees

Answer 25

ok so then it is 240 and 300

Answer 26

yes