Geometry

Cosine is adjacent over hypotenuse. The easiest way to do this would be to think of a 30, 60, 90 triangle in the unit circle. The side adjacent to the 30 degree angle is opposite the 60 degree side, so sqrt(3) in length, and the hypotenuse is 2. So Cosine(30) = sqrt(3)/2

kainarm:

How do you find the cosine of 30 in simplest radical form?

Many teachers think that you should just memorize the ratios for 30, 60 and 90
I'm with Bigsk, I work it out (very quickly) every time.

for the 30 and 60 ratios

I start with a equilateral triangle with side length 2 units. (all the angles are 60 degrees)
then I drop a perpendicular down from the top and that creates 2 identical right angled triangles. The two top angles are now 30degrees each.
The bottom sides are 1 unit each,
The hypotenuse is 2 units
Use pythagoras to get the other side sqrt(4-1) = sqrt3
Now you can read all the 30 and 60 degree ratios straight off the triangle.

Thanks for your suggestion. I really appreciate that you took all this time to try and help us. Keep up the good work. Keep on taking action.

Collen414:

Thanks for your suggestion. I really appreciate that you took all this time to try and help us. Keep up the good work. Keep on taking action.

Thanks Collen414,
I like doing this. I hope I am helping many people learn and appreciate mathematics. It is really nice to be thanked sometimes though.

Bigsk15 has been answering quite a few questions lately and he/she gives good answers.
so I will take this opportunity to thank Bigsk15.
There are starting to be too many questions for me to answer by myself and I appreciate that you are helping (helping me and all the forum users.)