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Popular >

2sin^2(θ)+1=3sin(θ)

Solution

2 sin^{2} (θ) + 1 = 3 sin (θ)

Solution

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

+1

Solution steps

2 sin^{2} (θ) + 1 = 3 sin (θ)

Solve by substitution

sin (θ) = 1, sin (θ) = \frac{1}{2}

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

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

Combine all the solutions

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

Popular Examples

sin^2(x)= 1/2 ,0<= x<= 2pi

sin^{2} (x) = \frac{1}{2}, 0 \leq x \leq 2 π

sin(3θ)=1,0<= θ<2pi

sin (3 θ) = 1, 0 \leq θ < 2 π

cos(2x)cos(x)-sin(2x)sin(x)=(sqrt(3))/2

cos (2 x) cos (x) - sin (2 x) sin (x) = \frac{3}{2}

sin(2x)cos(x)=sin(x)

sin (2 x) cos (x) = sin (x)

tan (\frac{1}{2} x) - 1 = 0

Frequently Asked Questions (FAQ)

What is the general solution for 2sin^2(θ)+1=3sin(θ) ?
The general solution for 2sin^2(θ)+1=3sin(θ) is θ= pi/2+2pin,θ= pi/6+2pin,θ=(5pi)/6+2pin