Question

How do you find the exact value of `2cos^2x+cosx-1=0` in the interval `0<=x<360`?

Answer 1

`x=60^@,180^@,300^@`

Explanation:

`"this is a quadratic in cos which is factored in the same"`
`"way as a usual quadratic"`

`2cos^2x+cosx-1=0`

`(2cosx-1)(cosx+1)=0`

`2cosx-1=0rArrcosx=1rArrcosx=1/2`

`rArrx=60^@" or "x=(360-60)^@=300^@`

`cosx+1=0rArrcosx=-1rArrx=180^@`

`"solutions are "x=60^@,180^@,300^@tox in[0,360)`