solve for x

Question

6tanx - 4sinx = 1

i tried it but got a quartic formula :S

16sin^4x + 8sin^3x + 37sin^2x - 36 = 0

Answer 1

This is a "nasty" problem and it does not simplify easily.
I don't know how you got your quartic equation.

I rewrote it as 6tanx = 1 + 4sinx
then graphed f(x) = 6tanx and
g(x) = 1+ 4sinx

There are two intersection points, one in quadrant I and another in quadrant III.

After a few iterations, I got x= 23.27º to come pretty close.

This is way beyond any highschool level I know, where did you get that question ?

Answer 2

I got the quartic by moving the sin to the right, squaring both sides, then multiplying everything by sin^2 and then changing the cos to sin.

My friend gave me this question, and he got it from his virtual school for gr 12 advanced functions lol.