Trig Equation

[vanbeersj]

I need to solve this equation

cos ø sin2 ø - sin ^3 ø = 0, find ø if 0< ø < 90°

The exponent 3 has me confused. I know I can substitue 2sinøcosø for the sin2ø then I'll have

cosø 2sinøcosø but I'm lost as to what to do with the sin^3ø.
I'm learning from home and my text doesn't do a good job of explaining.

 

[Deleted member 4993]

I need to solve this equation

cos ø sin2 ø - sin ^3 ø = 0, find ø if 0< ø < 90°

The exponent 3 has me confused. I know I can substitue 2sinøcosø for the sin2ø then I'll have

cosø 2sinøcosø but I'm lost as to what to do with the sin^3ø.
I'm learning from home and my text doesn't do a good job of explaining.

cos ø sin2ø - sin ^3 ø = 0

sin? (2cos[sup:59qo0vuh]2[/sup:59qo0vuh]? - sin[sup:59qo0vuh]2[/sup:59qo0vuh]?) = 0

Sin? cannot be equal to zero since 0 < ? < 90° ? 2cos[sup:59qo0vuh]2[/sup:59qo0vuh]? - sin[sup:59qo0vuh]2[/sup:59qo0vuh]? = 0 ? tan[sup:59qo0vuh]2[/sup:59qo0vuh]? = 2

Now you can solve it.....

 

[galactus]

\(\displaystyle cos(x)sin(2x)-sin^{3}(x)=0\)

\(\displaystyle 2cos^{2}(x)sin(x)-sin^{3}(x)=0\)

\(\displaystyle 2(1-sin^{2}(x))sin(x)-sin^{3}(x)=0\)

\(\displaystyle 2sin(x)-3sin^{3}(x)=0\)

Now, let \(\displaystyle u=sin(x)\) and turn it into a solvable cubic, then resub.

Just one way.