Solve the equation in the interval [0,360) for 11sin^2x-7sinx=2

Question

it needs to be done without a calculator.. 

Answer 1

11sin²x-7sinx=2

11sin²x-7sinx-2=0

use the quadratic formula

x=(7±√(49+88))/22

x=(7±√137)/22

x=(7±11.7047)/22

x=18.7047/22 and x=-4.7047/22

x=0.850214 and x=-0.21385

use arcsin to determine the angles

sin^-10.850214=58.2349º

sin^-1(-0.21385)=347.652º

put the decimal numbers into the equation to determine that you get a true statement

Answer 2

11sin² x - 7sin x = 2

11sin²x - 7sin x - 2 = 0

 

Not factorable over the set of rationals