What is the general solution for 2sin(θ)=-0.684 ?

The general solution for 2sin(θ)=-0.684 is θ=-0.34904…+2pin,θ=pi+0.34904…+2pin

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2sin(θ)=-0.684

2 sin (θ) = - 0.684

θ = - 0.34904 \dots + 2 πn, θ = π + 0.34904 \dots + 2 πn

Degrees

θ = - 19.99877 \dots^{\circ} + 36 0^{\circ} n, θ = 199.99877 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 sin (θ) = - 0.684

Divide both sides by

2

2 sin (θ) = - 0.684

Divide both sides by

2

\frac{2 sin ( θ )}{2} = \frac{- 0.684}{2}

Simplify

\frac{2 sin ( θ )}{2} = \frac{- 0.684}{2}

Simplify

\frac{2 sin ( θ )}{2} : sin (θ)

\frac{2 sin ( θ )}{2}

Divide the numbers:

\frac{2}{2} = 1

= sin (θ)

Simplify

\frac{- 0.684}{2} : - 0.342

\frac{- 0.684}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{0.684}{2}

Divide the numbers:

\frac{0.684}{2} = 0.342

= - 0.342

sin (θ) = - 0.342

sin (θ) = - 0.342

sin (θ) = - 0.342

Apply trig inverse properties

sin (θ) = - 0.342

General solutions for

sin (θ) = - 0.342

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

θ = arcsin (- 0.342) + 2 πn, θ = π + arcsin (0.342) + 2 πn

θ = arcsin (- 0.342) + 2 πn, θ = π + arcsin (0.342) + 2 πn

Show solutions in decimal form

θ = - 0.34904 \dots + 2 πn, θ = π + 0.34904 \dots + 2 πn

sec (a) (1 + sin (- a)) (sec (a) - tan (- x)) = 1

5 cos (x) = 3

6 cos^{2} (x) - 5 sin (x) = 2

arccos (2 x) = \frac{π}{3}

2 tan (x) = 2

What is the general solution for 2sin(θ)=-0.684 ?
The general solution for 2sin(θ)=-0.684 is θ=-0.34904…+2pin,θ=pi+0.34904…+2pin