Question

Write (sin13+sin167+cos13+cos167)(sin13-sin167+cos13-cos167) in the form asinx. No calculators.
Thank you!

Answer 1

sin 13 = sin 167 because sin is positive in second quad
cos 13 + cos 167 = 0 because cos is negative in the second quad

Answer 2

i can get it down to 4sin13cos13 don't know how to put it solely in the form of asinx

Answer 3

so it becomes (sin13+sin167)(cos13-cos167), and then..

Answer 4

sin 13 = sin 167 so (sin 13 +sin 167 ) = 2sin 13

Answer 5

cos13 = -cos167 so cos 13 - cos 167 = 2cos13

Answer 6

there's a reduction formula that says sin(0.5pi - theta) = costheta

Answer 7

this is where i have to get off. hope that helped.

Answer 8

yes it did. thanks!

Answer 9

sin(90-13) = cos13
is that right?

Answer 10

Yes, that's right.