Question

sin (x/2) = -cos (x)

Answer 1

Solving for x?

Answer 2

how

Answer 3

sorry but i don't get it

Answer 4

\[Identity:~~~~~~\sin(\frac{x}{2})~=~±\sqrt{\frac{1-\cos(x)}{2}}\]

Answer 5

ok , then how would you solve for x ?

Answer 6

I'm stupid, Sorry !!!

Answer 7

lets rewrite it,
\[-\cos(x)=\sqrt{\frac{1-Cos(x)}{2}}~~~~~~~~~~~~square~~both~~sides,\]\[Cos^2x=\frac{1-Cos(x)}{2}~~~~~~~~~~~~~~~~~~~`~both~~sides~~times~~2,\]\[2Cos^2x=1-Cos(x)\]\[Let~~~~Cos(x)=a,~~~~Do~~i t.\]

Answer 8

x is an angle

Answer 9

So it will now be\[2a^2=1-a,~~~~~~add~~a,~~and~~then~~subtract~~1~~~~~~from~~both~~sides.\]

Answer 10

Lets first solve for a, or for cosx, and whet we get for a, substitute into cosx=a

Answer 11

so what will be the angle ?

Answer 12

Solve for a.

I'll do it in my had, I'll use quadratic.