My teacher asked for the EXACT VALUES of

Question

sin(pi/6)
cos(pi/4)
csc(pi/3)

I have to figure it out without a calculator?
Also, if I was to do with it with a calculator, would csc be typed as 1/sin?

Answer 1

These are a few standard angles whose trig values it will be worth your time to learn. It is easy to find a table of common angles , and these will be listed, along with pi/2 and 0

pi/6: sin = 1/2 cos = √3/2 tan = 1/√3
pi/4: sin = cos = 1/√2 tan = 1
pi/3: sin = √3/2 cos = 1/2 tan = √3

Note that the co-functions of complementary angles are the same as the functions of the angle. e.g.

sin pi/6 = cos pi/3 because pi/6 + pi/3 = pi/2
sin pi/4 = cos pi/4

and yes, csc = 1/sin