What is the general solution for 2sin^2(θ)+3cos(θ)-3=0 ?

The general solution for 2sin^2(θ)+3cos(θ)-3=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=2pin

Popular >

2sin^2(θ)+3cos(θ)-3=0

2 sin^{2} (θ) + 3 cos (θ) - 3 = 0

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn, θ = 2 πn

Solution steps

2 sin^{2} (θ) + 3 cos (θ) - 3 = 0

Rewrite using trig identities

- 1 - 2 cos^{2} (θ) + 3 cos (θ) = 0

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = 1

cos (θ) = \frac{1}{2} : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

cos (θ) = 1 : θ = 2 πn

Combine all the solutions

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn, θ = 2 πn

3 sin (x) tan (x) + 3 sin (x) = 0

sin (z) + cos (z) = 2

12 sin^{2} (t) + cos (t) - 4 = 2

- 3 tan (θ) - 11 = 3 tan (θ) - 6

cos^{2} (x) - 6 cos (x) - 1 = 0

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