Question

How do you find the solution to `2sinthetacostheta+costheta=0` if `0<=theta<360`?

Answer 1

`theta in {90^@, 210^@,270^@, 330^@}`

Explanation:

Factoring the left side of
`color(white)("XXX")2sin(theta)cos(theta)+cos(theta)=0`
gives
`color(white)("XXX")color(red)(cos(theta)) * [color(blue)(2sin(theta)+1)] =0`

Which implies (for `theta in [0,360^@]`)
#{: ("either",color(red)(cos(theta)=0),or,color(blue)(2sin(theta)+1=0)), (,rarr color(red)(theta=90^@ or 270^@),,rarr color(blue)(sin(theta)= -1/2)), (,,,rarr color(blue)(theta= 210^@ or 330^@)) :}#