Question

Find all values of theta that satisfy the equation over the interval [0,2pi]. sin theta=-1/2

Answer 1

At what values of Theta, sin (theta) = - 1/2 ?

Answer 2

Yes

Answer 3

Can you tell me, what are the values of theta which give sin theta = - 1/2?

Answer 4

I'm not really sure how to do this problem

Answer 5

Can you tell me, what is sin(30) ?

Answer 6

1/2

Answer 7

Right, so, we need to find such a value of theta like 30 , which gives sin \(\theta\) = -1/2

If theta lies in the third quadrant and fourth quadrant, then sin theta is negative .

Answer 8

So, what we need here is negative sign in sin(30) , so, we will add 180 to 30 so that it comes in third quadrant :

sin(30+ 180) = sin(210) = -1/2

And for theta to come in 4th quadrant,

sin(30 + 300) = sin(330 degrees) = -1/2

Answer 9

So, we can say, for theta = 210 and theta = 330 , we get sin(theta) = -1/2

Answer 10

Why do you add it by 180 and 300?

Answer 11

See, if I will add 180 to it then it will automatically come to third quadrant and I actually used the following identity :

sin(180 + theta) = - sin(theta)

So, sin(180 + 30) = - sin(30) = -1/2

Answer 12

How would you convert the values into radian form?

Answer 13

1 degree = pi radians/180

Answer 14

So would it be 7pi/6 and 11pi/6?

Answer 15

Yes, right!

Answer 16

Thank you so much for your help!