Question

How do you solve `5 sin^2 (alpha) - 11 sin (alpha) + 2=0`?

Answer 1

`alpha=11.54^@`

Explanation:

Let `sin(alpha)=x`
Hence we can write
`5x^2-11x+2=0`
or
`5x^2-10x-x+2=0`
or
`5x(x-2)-1(x-2)=0`
or
`(x-2)(5x-1)=0`
or
`x-2=0`
or
`x=2`
or
`5x-1=0`
or
`5x=1`
or
`x=1/5`
or
Out of the above two solutions `sinalpha=2` which is invalid
Hence
`sinalpha=1/5`
or
`alpha=sin^-1(1/5)`
or
`alpha=11.54^@`