SOLUTION: This is probably a really dumb question, but can you please help me to understand how sin 210(degrees) = -1/2 and cos 135 (degrees) = 1/square root of 2? I'm having a hard time

Question 180080: This is probably a really dumb question, but can you please help me to understand how sin 210(degrees) = -1/2 and cos 135 (degrees) = 1/square root of 2?
I'm having a hard time trying to justify these problems and I'm sure it's just something really simple that I'm missing. When trying to find the exact value of the above expressions, do I draw a rough sketch of the angle, or do I just use the standard 30, 60, 90 degree triangle to find the ratio? Thanks!
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Always, always draw the angle in the quadrant it belongs in.
The angle is a rotating vector with the sine or cosine wave
projected along the x-axis.
It helps if you can draw or at least picture the sine wave
as the vector rotates around the circle through the
quadrants. You really need this complete picture every time
and it's worth the effort
sin(210) = sin (180 + 30) = -(1/2)
It's in the 3rd quadrant where the sin is negative
cos(135) = cos(90 + 45) = -(1/)
It's in the 2nd quadrant where the cos is negative
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