# Homework Help: Cos x or sin x or tan x

1. Sep 20, 2004

### haribol

Assume you are given tan (pi/6). This means sin (pi/6)/cos (pi/6). But my question is, if you are given sin (pi/6) or cos (pi/6), is it possible to derive the numerical value without using calculator?

2. Sep 20, 2004

### Sirus

You can derive these based on a unit circle triangle (don't remember exactly), but in the end you just have to memorize them anyways for use in trig.

3. Sep 20, 2004

### swingkids

Yeah, you just have to memorize that crap. You won't need a calculator

4. Sep 20, 2004

### K.J.Healey

Or you can learn the expanded series notation(infinite series) and just start adding terms.

5. Sep 20, 2004

### HallsofIvy

Better: Construct an equilateral triangle,with each side of length 2, then drop a perpendicular from the top to the base. That line bisects the angle and the opposite side. Since all three angles of an equilateral triangle are pi/3 radians (or 60 degrees), half of it is pi/6 (or 30 degrees) , while half the base has length 1, we have a right triangle with side opposite the pi/6 angle of length 1, hypotenuse of length 2 and side "near" the pi/6 angle of length (use the Pythagorean theorem) &radic;(4- 1)= &radic;(3).

sin(pi/6)= opposite/hypotenuse= 1/2.

csc(pi/6)= hypotenuse/opposite= 2/1=2.

Of course, you can also use that to find the trig functions for pi/3, the other angle in the right triangle.

6. Sep 20, 2004

### haribol

Thanks a lot, all I've to do is play around with the equations now, thanks Hal and guys.