Sine and Cosine?

Question

I learned today in Precalculus about Sine and Cosine. I understood everything except this thing:

Sin 169 degrees- positive
Cos 210 degrees- negative
Sin (4 pi over 3) or 240 degrees- negative.

HOW DO YOU DETERMINE IF IT"S POSITIVE OR NEGATIVE?

Answer 1

Always remember
sine is positive between 0 to 180
cosine is positive between 0 to 90 and again between 270 to 360

see the table given in the source below

Answer 2

you just have to know hich quadrant the angle is. for example, a point in quadrant 2 will have a negative x and a positive y. for example, the point (-2, 3) in quadrant 2. the same goes for angles, if, for example, it's in quadrant 3, then it will have both negative x and y.
the thing is, solving for the cosine of an angle means solving for the x value of the point when that angle touches the circle. sine is for the y value of that point. for example, the angle 30 degrees has a cosine of 1/square root of two and a sine of 1/2. this means that the point where 30 degrees touches the circle is at the point (1/square root of 2, 1/2)
you'll notice that both the sine and cosine are positive. they're positive because the angle is in quadrant 1. a point in the first quadrant will always have positive values for the coordinates. so it all depends on the quadrant the angle is found in, since the point where it touches the circle is also in the same quadrant. just remember: cosine is for x, sine for y.
hope it helped.