What is the general solution for sin(θ)=-4/7 ?

The general solution for sin(θ)=-4/7 is θ=-0.60824…+2pin,θ=pi+0.60824…+2pin

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sin(θ)=-4/7

sin (θ) = - \frac{4}{7}

θ = - 0.60824 \dots + 2 πn, θ = π + 0.60824 \dots + 2 πn

Degrees

θ = - 34.84990 \dots^{\circ} + 36 0^{\circ} n, θ = 214.84990 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = - \frac{4}{7}

Apply trig inverse properties

sin (θ) = - \frac{4}{7}

General solutions for

sin (θ) = - \frac{4}{7}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

θ = arcsin (- \frac{4}{7}) + 2 πn, θ = π + arcsin (\frac{4}{7}) + 2 πn

θ = arcsin (- \frac{4}{7}) + 2 πn, θ = π + arcsin (\frac{4}{7}) + 2 πn

Show solutions in decimal form

θ = - 0.60824 \dots + 2 πn, θ = π + 0.60824 \dots + 2 πn

6 cos (6 x) = 5

4 sec (x) + 23 = sec (x)

sec (x) sin (x) = 2

sec (x) cot (x) = \frac{7}{6}

tan (x) cos (x) = 0

What is the general solution for sin(θ)=-4/7 ?
The general solution for sin(θ)=-4/7 is θ=-0.60824…+2pin,θ=pi+0.60824…+2pin