Question

solve 1/2 - sin x=1

Answer 1

First, try to see what sin x would have to be (hint: 1/2 - -1/2 = 1)

Answer 2

1

Answer 3

Yes, so this means sin x = -1/2, because 1/2 - - 1/2 = 1.
Now you have to solve:

sin x = -1/2. Do you know how to do that?

Answer 4

no

Answer 5

It has to do with "known" (?) values of the sine function, e.g.

Everyone has to remember that:

sin 0 = 0
sin(pi/6)= 1/2
sin((pi/4)=1/2 sqrt(2)

Do you know these values also?

Answer 6

kinda

Answer 7

im new to this stuff

Answer 8

But you know about the unit circle, not?

Answer 9

yes

Answer 10

OK, I'll draw one for you with sin x = -1/2, hold on, please

Answer 11

Almost done ;)

Answer 12

This is the unit circle.

Answer 13

Definition of sin:

If you want to know what the sine of a number (angle) is, do this: draw the angle from the positive x-axis, in anti-clockwise direction. The angle meets the circle in a certain point.
The y-coordinate of that point is the sine of the angle.

In my drawing, I have done it the other way round, because I already know the sine, but not the angle. So I've drawn a horizontal line at height -1/2. Where it intersects the unit circle, lines to the origin have been drawn.
Now you can see there are two angles, alpha and beta, that will have a sine of -1/2.

Does this make any sense to you?

Answer 14

yes

Answer 15

x= pi?

Answer 16

Ok, If you look at the bottom half of the circle, you'll see alpha and beta. What are their values? The triangles there must look familiar!

They are 30-60-90 degree triangles (don't know how you call them, but they are well known...)

Answer 17

So \[\alpha = -30 \deg =-\frac{ \pi }{ 6 }\]

Answer 18

so its - pi/6?

Answer 19

Yes, and the other one is 180+30=210 degrees, or 7pi/6