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Popular >

3sin^2(x)-3sin(x)+cos^2(x)=0

Solution

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

Solution

x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

+1

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 1, sin (x) = \frac{1}{2}

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Popular Examples

12cos^2(x)-7cos(x)+1=0

12 cos^{2} (x) - 7 cos (x) + 1 = 0

tan(x/2)tan(x)=-3

tan (\frac{x}{2}) tan (x) = - 3

sin(-x)=-1/3 ,tan(x)=-(sqrt(2))/4

sin (- x) = - \frac{1}{3}, tan (x) = - \frac{2}{4}

solvefor x,h=tan(x-pi/6)solve for

x, h = tan (x - \frac{π}{6})

sec(θ)+1/(cot(θ))=1

sec (θ) + \frac{1}{cot ( θ )} = 1

Frequently Asked Questions (FAQ)

What is the general solution for 3sin^2(x)-3sin(x)+cos^2(x)=0 ?
The general solution for 3sin^2(x)-3sin(x)+cos^2(x)=0 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin