Math Is Fun Forum

redXI

Member

Registered: 2008-02-24

Posts: 3

Please confirm <circular function trigonometry)

Solutions to 2 sin 2x = -3^1/2

First, I simplify the trigonometric equation:

sin 2x = (-3^1/2)/2  ---- 0<2x<720 degrees

...find the basic angle which is 60 degrees

Find the values of 2x between 0 and 4pi that satisfy that equation, this is the part where I get lost:

2x = 180+60, 36--60, 360+180+60, 360+360-60 degrees

x = 120, 150, 240, 330 degrees

Now, I only wonder how to input proper 180 and 360 degrees to get the X?? How  come in some part the 60 degrees is positive and some negative? Thanks.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Please confirm <circular function trigonometry)

On a unit circle, at 60 degrees from the center going at about one-o'clock, you hit
the circle.  Your height is what part of one, if one is the radius.
This height is the sine of 60 degrees.
It is

.  I don't know why, but memorize it:  0.866, half of 1.732

---

igloo myrtilles fourmis