Question

(Sinx)(Cosx)=1/2Cosx
how do you solve this for the degree measures?

Answer 1

sin(x)*cos(x) = 1/2*cos(x)


2*sin(x)*cos(x) = cos(x)


2*sin(x)*cos(x) - cos(x) = 0


cos(x) ( 2*sin(x)-1 ) = 0


cos(x) = 0 or 2*sin(x)-1 = 0


cos(x) = 0 or sin(x) = 1/2


x = arccos(0) or x = arcsin(1/2)


x = 90 + 180*k, x = 30 + 360*k, or x = 150 + 360*k, where k is an integer.

Answer 2

when you multiplied the two to both sides, why don't you give the two to both sin and cos?

Answer 3

Because I'm not distributing the 2. If it were sin(x) + cos(x), then that would apply.

Answer 4

oh makes sense, so you would distribute when theirs a minus or plus sign.

Answer 5

Exactly, but when there's a minus sign between two terms (to indicate subtraction)

Answer 6

thank you.

Answer 7

you're welcome