If given the values of cos 2 and cos 3, sin 2 and sin 3, which of the following can be found arithmetically?

Question

2369 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-30T10:37:05

All of them

First

#cos(1) = cos(3-2)#, and

#cos(a-b) = sin(a) sin(b) + cos(a) cos(b)#

which are all known.

Second

#cos(5) = cos(3+2)#, and

#cos(a+b) = cos(a) cos(b) - sin(a) sin(b)#

which are all known.

Third

#sin(-1)=sin(2-3)#, and

#sin(a-b) = sin(a) cos(b) - cos(a) sin(b)#

which are all known.

Fourth

This is the same as point #2#, with #a=pi# and #b=2#.

Fifth one: yes

#tan(4) = \frac{sin(4)}{cos(4)} = \frac{sin(2+2)}{cos(2+2)}#

And find #sin(4)# and #cos(4)# using again the formulas for #sin(a+b)# and #cos(a+b)# plugging #a=b=2#.