What is the general solution for 5sin(θ)-4=2sin(θ)-6 ?

The general solution for 5sin(θ)-4=2sin(θ)-6 is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin

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5sin(θ)-4=2sin(θ)-6

5 sin (θ) - 4 = 2 sin (θ) - 6

θ = - 0.72972 \dots + 2 πn, θ = π + 0.72972 \dots + 2 πn

Solution steps

5 sin (θ) - 4 = 2 sin (θ) - 6

Solve by substitution

sin (θ) = - \frac{2}{3}

sin (θ) = - \frac{2}{3} : θ = arcsin (- \frac{2}{3}) + 2 πn, θ = π + arcsin (\frac{2}{3}) + 2 πn

Combine all the solutions

θ = arcsin (- \frac{2}{3}) + 2 πn, θ = π + arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

θ = - 0.72972 \dots + 2 πn, θ = π + 0.72972 \dots + 2 πn

cos (2 θ) - cos (4 θ) = 0

tan (x) = 1.4

sin (θ) = 0.71

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

tan (x) = \frac{8}{6}

What is the general solution for 5sin(θ)-4=2sin(θ)-6 ?
The general solution for 5sin(θ)-4=2sin(θ)-6 is θ=-0.72972…+2pin,θ=pi+0.72972…+2pin