# never learned how to change a cosine into frational form

• Jan 12th 2011, 01:59 PM
never learned how to change a cosine into frational form
I was wondering if someone could help me out with how to change a cosine into fractional from: example cos 45 = sqrt2/2 and cos 150 = sqrt3/2

I know that if I take the inverse of the cosine decimal form I can take the answer do square it, make a fraction out of it with the sqrt of the square dived by the squared number. that gets really messy as well though.
• Jan 12th 2011, 02:04 PM
pickslides
Are you saying...

When solving $x = \cos 45^o$ , how can you get a fractional answer rather than some nasty decimal?
• Jan 12th 2011, 02:06 PM
yeah, I can do it the way I explained but with most angles, that will still achieve a nasty decimal
• Jan 12th 2011, 02:10 PM
pickslides
Only particular angles will give you something nice.

In general these are 0,30,45,60,90 and multiples of these. You can achieve a rational answer for others, but start by working on these ones first.

Have you seen the special triangles?
• Jan 12th 2011, 02:14 PM
I haven't seen the special triangles.
• Jan 12th 2011, 02:19 PM
pickslides
They are my favourite triangles. Commit them to memory and you will be a trig-wiz!

Special Triangles
• Jan 12th 2011, 02:20 PM
e^(i*pi)
Essentially your construct a triangle with angles 60-30-90 and 45-45-90

Special right triangles - Wikipedia, the free encyclopedia
• Jan 12th 2011, 02:29 PM