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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Popular Trigonometry >

sin(θ/2)=(7.83)/(2(4.35))

Solution

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

Solution

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

Degrees

θ = 128.31613 \dots^{\circ} + 72 0^{\circ} n, θ = 231.68386 \dots^{\circ} + 72 0^{\circ} n

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

sin (\frac{θ}{2}) = \frac{7.83}{8.7}

General solutions for

sin (\frac{θ}{2}) = \frac{7.83}{8.7}

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

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

\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

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

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

Simplify

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Divide the numbers:

\frac{2}{2} = 1

= θ

Simplify

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

2 arcsin (\frac{7.83}{8.7}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 arcsin (\frac{7.83}{8.7}) + 4 πn

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

θ = 2 arcsin (\frac{7.83}{8.7}) + 4 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

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

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

Simplify

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Divide the numbers:

\frac{2}{2} = 1

= θ

Simplify

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

2 π - 2 arcsin (\frac{7.83}{8.7}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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