Question

Find solutions, exact where possible, to the following over the domain [0,2π].

2 sin (x) + 0.893 = 0

Answer 1

2sinx = -0.893
sinx = -0.893 / 2
the negatvie sings tell that is in 3rd and 4th quadrant as sin is negative in it.
x =sin^-1 (-0.893/2)

Answer 2

ok, I think I know where I went wrong, I used 1st and 2nd quadrant, thanks, let me try again first.

Answer 3

sure :).. you just have to keep in mind where the value is positive and where negative..

Answer 4

hmm, somehow I still got the wrong answers, can you help me?

Answer 5

sure .. tell me what u have done so far..

Answer 6

so x = -0.4628
then in the 3rd quadrant it would be π-0.4628 = 2.679
and in the 4th quadrant it would be 2π+0.4628 = 6.746

Answer 7

hmm no.. x = -0.4628
negative sign here just tell us the quadrant in which the value lies. after we know where the value lies we can ignore the negative sign. so now we take x = 0.4628
3rd Quad = π + 0.4628
4th Quad = 2π - 0.4628

Answer 8

oh k, no wonder! thanks and sorry my internet is lagging real bad for some odd reason.

Answer 9

no worries.. same happens with my net. :)

Answer 10

one question, why can you ignore the negative sign?

Answer 11

like after you find which quadrant it lies in.

Answer 12

because negative sign is just for letting us know.. like if u are getting a negative value of sin .. means we know sin has a negative value in those quadrants.. and well not sure for reason but i think normally when we do on graph we measure angle by going anticlockwise direction.. negative sign tell us to reach it from the clock wise direction..making the value of x positive as we are measuring angle in clockwise direction.