# Thread: never learned how to change a cosine into frational form

1. ## 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.

2. Are you saying...

When solving $\displaystyle x = \cos 45^o$ , how can you get a fractional answer rather than some nasty decimal?

3. yeah, I can do it the way I explained but with most angles, that will still achieve a nasty decimal

4. 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?

5. I haven't seen the special triangles.

6. They are my favourite triangles. Commit them to memory and you will be a trig-wiz!

Special Triangles

7. Essentially your construct a triangle with angles 60-30-90 and 45-45-90

Special right triangles - Wikipedia, the free encyclopedia

8. awesome, thanks a bunch

9. You can also google the unit circle.

10. A side note: Most of those decimal answers you are getting are not exact answers. They are only approximations (although good approximations) to the actual answers. The actual answers are irrational and therefore cannot be written as finite decimals.