Question

Resolva a equação 2 cos2 x−3sin x−3=0 2cos2x-3sinx-3 = 0no intervalo 0⩽x⩽2π

Answer 1

2cos²x-3sinx-3=0

sin ²x+cos ²x=1

cos²x=1-sin²x

2(1-sin²x)-3sinx-3=0

2-2sin²x-3sinx-3=0

sinx=n

2-2n²-3n-3=0

-2n²-3n-1=0

n=3+-√9-8/-4

n=-3+-1/4

n'=-3+1/4=-1/2

n"=-3-1/4=-1

Sinx''=-1

x"=270°

x"=3π/2

sinx'=-1/2

x'=330

x'=33π/18

S:{3π/2,33π/18}