Solve the equation? (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.) 4 sin^2(x) + 6 sin(x) + 2 = 0

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Answer 1 · 2018-03-30T08:13:13

#color(blue)((3pi)/2+n2pi)#

#color(blue)((7pi)/6+n2pi)#

#color(blue)((11pi)/6+n2pi)#

#4sin^2x+6sinx+2=0#

Let #u=sinx#

#4u^2+6u+2-0#

Factor:

#(2u+2)(2u+1)=0=>u=-1 and u=-1/2#

#u=sinx#

#sinx=-1#

#x=arcsin(sinx)=arcsin(-1)=(3pi)/2+n2pi#

#sinx=-1/2#

#x=arcsin(sinx)=arcsin(-1/2)=(7pi)/6+n2pi, (11pi)/6+n2pi#

Solutions:

#color(blue)((3pi)/2+n2pi)#

#color(blue)((7pi)/6+n2pi)#

#color(blue)((11pi)/6+n2pi)#