Use a graphing utility to approximate the solutions to three

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval [0, 2pi] 20 sin^3 x + 10 sin^2 x - 10 sin x - 5 = 0 x = Find the x-intercepts of the graph. y = sin pi x/6 + 1 x =

Solution

20sin³x+10sin²x-10sin x-5=0

10sin²x(2sinx+1)-5(2sinx +1)=0

(10sin²x-5)(2sinx+1)=0

10sin²x-5=0      and   2sinx+1=0

sin²x=1/2         and     sinx=-1/2

sin x=+-1/sqrt2     and    sin x= -1/2

x=sin^-1 (+-1/sqrt2)    and x=sin^-1(-1/2)

x=pi/4, 3pi/4, 5pi/4,7pi/4    and x= 7pi/6,11pi/6

x=pi/4,3pi/4,7pi/6,5pi/4,7pi/4,11pi/6