Question

solve 3sine x -4sine^3 x = sqrt(3)/2

Answer 1

\(\LARGE\color{black}{ 3\sin(x) -4\sin^3(x)=\frac{\sqrt{3}}{2} }\)

Answer 2

\(\LARGE\color{black}{ \sin(x)(3 -4\sin^2x)=\frac{\sqrt{3}}{2} }\)

can you solve the first part when it is equivalent to sin(x)?

Answer 3

i got that far but im not sure how to continue

Answer 4

\(\LARGE\color{black}{ \sin(x)(3 -4\sin^2x)=\frac{\sqrt{3}}{2} }\)

\(\Large\color{black}{ \sin(x)=\frac{\sqrt{3}}{2} }\) or \(\Large\color{black}{ 3 -4\sin^2x=\frac{\sqrt{3}}{2} }\)

Answer 5

can you solve the first, the left part?

Answer 6

for some reason i was to further factor 3-4sine^2x

Answer 7

so x = arcsine(sqrt3/2), arcsine (+/- sqrt( ((sqrt3/2) -3) / 4)

Answer 8

you can't find the x, sine of which is sqrt{3}/2, is that your trouble?
Draw a 30-60-90 \(\large\color{black}{ \triangle }\).

Answer 9

beacuse the hyp is smaller than opp