Question

how to use unit circle to calculate sin 300?

Answer 1

well, are you most familiar with the unit circle in terms of degrees or radians?

Answer 2

a bit. it is hard to memorise though

Answer 3

let's just do it in degrees then.
Remember that you can always convert an angle to radians by multiplying by pi/180

Answer 4

But anyway...

Answer 5

First of all, we need to figure out which type of angle 300 degrees is
Let me draw it:

Answer 6

There, it will look like that. ^

Answer 7

From that picture we can see it will be 60 degrees below the x-axis.

Answer 8

how does that knowledge help us?
Which first-quadrant angle is it similar to?

Answer 9

If we reflect it over the x-axis, what angle will it be? @ozhobbits

Answer 10

if 300 degrees is 60 degrees _below_ the x-axis,
if we reflect it, the angle we get will be 60 degrees _above_, right?

Answer 11

yeah

Answer 12

so what that means is that our 300-degree angle will have the same sine and cosine as a 60-degree angle, except for the signs
since, clearly, the sine of an angle below the x-axis has to be negative

Answer 13

so then if we know the sine of 60 degrees, all we need to do to get the sine of 300 degrees is to add a negative sign.

What will it be? @ozhobbits

Answer 14

and



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