Question

Find two common angles that either add up to or differ by 7pi/12. Rewrite this problem as the cosine of either a sum or a difference of these two angles.

Answer 1

I have found two common angles, but I have no idea what the question means by rewriting it as the cosine of the two angles.

Answer 2

Ok, the angle in degrees is 105. If I were to rewrite that as a sum in terms of the cosine function, I would do something like this:\[\cos(A+B)-->\cos(45+60)\]We are familiar with the cosine of both the 45 degree angle and the 60 degree angle. That's what it means by rewriting it as the cosine of two angles. What are your angles in radians?

Answer 3

So it would be cos(pi/4 + pi/3)?

Answer 4

Your first one would be, in radians,\[\cos(\frac{ \pi }{ 4 }+\frac{ \pi }{3})\]

Answer 5

What was your other angle you said you found?

Answer 6

And that would equal cos(7pi/12)

Answer 7

Oh, that's what I meant by the two angles I found. pi/4 and pi/3

Answer 8

You could use that identity to find the exact value of cos(7pi/12). It's a way of going about finding exact measures of angles you aren't familiar with by putting it into terms of angles you ARE familiar with. That's the point of this identity.

Answer 9

Ok, then let me do a bit of thinking on this ok? BRB

Answer 10

I think if you just added 180 to both those angles you would have an equivalency of 45+60 (or your radian measures), so you could use\[\cos(\frac{ 9\pi }{ 4 }+\frac{ 4\pi }{3 })\]

Answer 11

Unless you HAVE to use a difference as well as a sum?

Answer 12

Hm, I just calculated it and cos(pi/4 + pi/3) is equivalent to 7pi/12. Thank you for your help! :D

Answer 13

You're welcome!