hey my teacher requires us to be able to evaluate arcsines and arccosines and arctangents without a calculator (exact values). I know how to do it with the unit circle points (pi/4, pi/3, etc.) but not with other, random values. Can anyone help?
hey my teacher requires us to be able to evaluate arcsines and arccosines and arctangents without a calculator (exact values). I know how to do it with the unit circle points (pi/4, pi/3, etc.) but not with other, random values. Can anyone help?
You can't! Not with random values and I am sure your teacher does not expect you to find, say $\displaystyle cos^{-1}(3/5)$. As far as this particular question, $\displaystyle cos(x)= -1/\sqrt{2}$, if, as you say, you know "(pi/4, pi/3, etc.)" then this should be easy. cos(t) is the x coordinate of a point on the unit circel so draw a vertical line at $\displaystyle x= -1/\sqrt{2}$ and think about the symmetry of the circle.