How Do You Isolate sin a in a Quadratic Trigonometric Equation?

[ditto_299]

So, I know how to solve them in general, but this one in particular, what do you do when the sin or cos etc is squared?

6sin^2 a - 11sin a + 4 = 0 , domain is from -360 until 360 degrees

we learned that, you need to isolate sin a, and then find the possible angles. I just need to know how to isolate sin a.

so i thought maybe this...

6 (sin a + sin a) - 11sin a = -4

but i don't know from here on...
please help! exam is coming up!

 

[HallsofIvy]

So, I know how to solve them in general, but this one in particular, what do you do when the sin or cos etc is squared?

6sin^2 a - 11sin a + 4 = 0 , domain is from -360 until 360 degrees

we learned that, you need to isolate sin a, and then find the possible angles. I just need to know how to isolate sin a.

so i thought maybe this...

6 (sin a + sin a) - 11sin a = -4

What? sin^2 a is (sin a)(sin a) NOT "sin a+ sin a"?

but i don't know from here on...
please help! exam is coming up!

Perhaps it would be simpler to replace sin a by y:
6y^2- 11y+ 4= 0. Can you solve that quadratic equation? After finding solutions, that is, specific values for y, you can solve sin a= y.