Question

Question #1d7ab

Answer 1

`S={pi/6,(5pi)/6}`

Explanation:

Note that this equation looks like a quadratic equation but instead of x we have sin x and a=4, b= -4, and c= 1, so we will use the quadratic formula to solve. That is,

`x=(-b+-sqrt(b^2-4ac))/(2a)`. Therefore,

`sinx =(4+- sqrt(16-4(4)(1)))/(2*4)`

`=(4+-sqrt(16-16))/8`

`=4/8`

`sin x = 1/2`

`x=sin^-1(1/2)`

`x=pi/6 + 2pin or x=(5pi)/6+2pin`

Put in `n=0` we have `x=pi/6 or x= (5pi)/6`

Note that if we put in any other n value the answers will fall outside of the restriction `[0,2pi)`. Hence, our solution set is

`S={pi/6,(5pi)/6}`