Hi

Find all exact solutions on [0,2pi)

2(cos^2)x + 3sinx = 3

Someone said i had to use (cos^2)x + (sin^2)x = 1 and use sin x as a variable, but i do not understand what that means.

Can someone explain to me step by step?

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- Jul 29th 2010, 06:35 AMdanielh9103Precalculus Help. Finding exact solutions on the equation
Hi

Find all exact solutions on [0,2pi)

2(cos^2)x + 3sinx = 3

Someone said i had to use (cos^2)x + (sin^2)x = 1 and use sin x as a variable, but i do not understand what that means.

Can someone explain to me step by step? - Jul 29th 2010, 06:43 AMeumyang
Exactly what that person said. Use sin x as a variable.

Replace with :

See how this looks like a quadratic? If you replaced with you would get

Solve the quadratic for y, plug back in for y, and solve for x. - Jul 29th 2010, 06:59 AMdanielh9103
thank you!

so i factored out 2(sin^2)x - 3 sinx + 1 = 0

i got (sinx -1) (sin x - 1)

set them equal to zero and got sin x = 1

making x = pi/2 - Jul 29th 2010, 07:02 AMeumyang
- Jul 29th 2010, 07:12 AMdanielh9103
im sorry! it was a typo!

(2 sinx -1) (sinx - 1)

sinx= 1/2 sinx = 1

x = pi/2, pi/6, 5pi/6 - Jul 29th 2010, 07:14 AMeumyang
Much better now! (Clapping)