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

Staff Emeritus
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.