## Edutopia 2 years ago question about the proof of trig addition formulas for cos:

1. Edutopia

sorry about the scrolling: http://en.wikipedia.org/wiki/Proofs_of_trigonometric_identities on the part with the diagram for trig addition formulas, where does "RPQ = (PI/2) - RPQ" come from?

2. Edutopia

also any sites with a better, easy to understand, definition would be greatly appriciated

3. AccessDenied

RPQ = pi/2 - RQP pi/2 radians is 90 degrees. RPQ = 90 degrees - RQP which we can see because that triangle is a right triangle, so the other two angles have to be complementary to add up to 180 degrees interior.

4. Edutopia

but PRQ is only one of the complementary angles, how do i know that it is half of 90?

5. AccessDenied

I believe PRQ is meant to be a right angle, 90 degrees or pi/2 radians, although it doesn't appear to be indicated as such...

6. AccessDenied

|dw:1357875756276:dw| Just drawing diagram here

7. Edutopia

im sorry we got it switched around somewhere its RPQ not PQR

8. Edutopia

they are proving that RPQ=alpha

9. AccessDenied

Since PRQ is a right triangle with right angle PRQ, RPQ and RQP are complementary. <RPQ + <RQP + <PRQ = 180 <RPQ + <RQP + 90 = 180 <RPQ + <RQP = 90 <RPQ = 90 - <RQP Would that make sense?

10. Edutopia

OH RPQ is a TRIANGLE! oops

11. AccessDenied

the pi/2 is just radians, i was using degrees. sorry if that is confusing...

12. Edutopia

no its not i understand radians

13. AccessDenied

Ah, okay. :)

14. Edutopia

aha i see it, thank you very much!

15. AccessDenied

You're welcome! :)