What is the general solution for sin(θ/2)=(7.83)/(2(4.35)) ?

The general solution for sin(θ/2)=(7.83)/(2(4.35)) is θ=2*1.11976…+4pin,θ=2pi-2*1.11976…+4pin

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sin(θ/2)=(7.83)/(2(4.35))

sin (\frac{θ}{2}) = \frac{7.83}{2 ( 4.35 )}

θ = 2 \cdot 1.11976 \dots + 4 πn, θ = 2 π - 2 \cdot 1.11976 \dots + 4 πn

Solution steps

sin (\frac{θ}{2}) = \frac{7.83}{2 ( 4.35 )}

Multiply the numbers:

2 \cdot 4.35 = 8.7

sin (\frac{θ}{2}) = \frac{7.83}{8.7}

Apply trig inverse properties

\frac{θ}{2} = arcsin (\frac{7.83}{8.7}) + 2 πn, \frac{θ}{2} = π - arcsin (\frac{7.83}{8.7}) + 2 πn

Solve

\frac{θ}{2} = arcsin (\frac{7.83}{8.7}) + 2 πn : θ = 2 arcsin (\frac{7.83}{8.7}) + 4 πn

Solve

\frac{θ}{2} = π - arcsin (\frac{7.83}{8.7}) + 2 πn : θ = 2 π - 2 arcsin (\frac{7.83}{8.7}) + 4 πn

θ = 2 arcsin (\frac{7.83}{8.7}) + 4 πn, θ = 2 π - 2 arcsin (\frac{7.83}{8.7}) + 4 πn

Show solutions in decimal form

θ = 2 \cdot 1.11976 \dots + 4 πn, θ = 2 π - 2 \cdot 1.11976 \dots + 4 πn

- 4 sin (c) - 2 = sin (c) + 1

cot^{2} (x) + 1 = 2

sin (x) = \frac{1}{3}, sec (y) = \frac{25}{24 , cos ( x + y )}

2 = 2 - π cos (t)

a, 45 = arctanh (\frac{a}{b})

What is the general solution for sin(θ/2)=(7.83)/(2(4.35)) ?
The general solution for sin(θ/2)=(7.83)/(2(4.35)) is θ=2*1.11976…+4pin,θ=2pi-2*1.11976…+4pin