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# How do you find the angle, when given two angles, using the rotation matrix? watch

1. http://prntscr.com/ia1eap

what i have done:

using the rotation matrix,
cos^-1(-1/root2) = 135 degrees,
sin^-1(-1/root2) = -45 degrees.

i've got two angles and i don't know where to go from there. if they're both the same, then that's the angle but they're not. what do you do from here? if i can remember correctly, it's something to do with comparing sine and cosine graphs but i can't find anything on it from youtube, google or from my textbook.

the answer is 225 degrees anticlockwise from origin but i don't know how to get to the answer.
2. (Original post by num.7)
...
Note quite...

You have and
You can solve these for different values of , then pick the one which satisfies both.

Alternatively, note that cos is -ve when and sine is negative when so we know that our angle must be . Dividing one eq. by the other yields which you can solve for in that range.
3. (Original post by RDKGames)
Note quite...

You have and
You can solve these for different values of , then pick the one which satisfies both.

Alternatively, note that cos is -ve when and sine is negative when so we know that our angle must be . Dividing one eq. by the other yields which you can solve for in that range.
how do you solve these? i still don't understand.
4. (Original post by num.7)
how do you solve these? i still don't understand.
Have you covered solving trig equations like in the range for example? It's a C2 topic.
5. One could graph -1/root2 alongside a graph of cos x and sin x on a graphical calculator, and look for the point where all 3 intersect (given a certain range, i assume 0<x<2pi), that will be the angle that satisfies both.

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