Important Angles: 30°, 45° and 60°

You should try to remember sin, cos and tan for the angles 30°, 45° and 60°.

Yes, yes, it is a pain to have to remember things, but it will make life easier when you know them, not just in exams, but other times when you need to do quick estimates, etc.

These are the values you should remember!

Angle	Sin	Cos	Tan=Sin/Cos
30°			1√3 = √33
45°			1
60°			√3

How To Remember?

To help you remember, think "1,2,3" :

	sin(30°)  =	√1	=	1	(because √1 = 1)
		2		2

	sin(45°)  =	√2
		2

	sin(60°)  =	√3
		2

And cos goes "3,2,1"

	cos(30°)  =	√3
		2

	cos(45°)  =	√2
		2

	cos(60°)  =	√1	=	1	(because √1 = 1)
		2		2

Just 3 Numbers

In fact, knowing 3 numbers is enough:	1	,	√2	and	√3
	2		2		2

Because they work for cos as well as sin:

Well, tan = sin/cos so we can calculate it like this:

tan(30°) = sin(30°)  =  1/2  =  1 cos(30°) √3/2 √3		But writing 1/√3 may cost you marks (see Rational Denominators), so instead use √3/3
tan(45°) = sin(45°)  =  √2/2  = 1  cos(45°) √2/2
tan(60°) = sin(60°)  =  √3/2  = √3  cos(60°) 1/2