What is the general solution for 3/2 =2*25sin(θ/2) ?

The general solution for 3/2 =2*25sin(θ/2) is θ=2*0.03000…+4pin,θ=2pi-2*0.03000…+4pin

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3/2 =2*25sin(θ/2)

Solution

\frac{3}{2} = 2 \cdot 25 sin (\frac{θ}{2})

Solution

θ = 2 \cdot 0.03000 \dots + 4 πn, θ = 2 π - 2 \cdot 0.03000 \dots + 4 πn

Degrees

θ = 3.43826 \dots^{\circ} + 72 0^{\circ} n, θ = 356.56173 \dots^{\circ} + 72 0^{\circ} n

Solution steps

\frac{3}{2} = 2 \cdot 25 sin (\frac{θ}{2})

Switch sides

2 \cdot 25 sin (\frac{θ}{2}) = \frac{3}{2}

Divide both sides by

50

2 \cdot 25 sin (\frac{θ}{2}) = \frac{3}{2}

Divide both sides by

50

\frac{2 \cdot 25 sin ( \frac{θ}{2} )}{50} = \frac{\frac{3}{2}}{50}

Simplify

\frac{2 \cdot 25 sin ( \frac{θ}{2} )}{50} = \frac{\frac{3}{2}}{50}

Simplify

\frac{2 \cdot 25 sin ( \frac{θ}{2} )}{50} : sin (\frac{θ}{2})

\frac{2 \cdot 25 sin ( \frac{θ}{2} )}{50}

Multiply the numbers:

2 \cdot 25 = 50

= \frac{50 sin ( \frac{θ}{2} )}{50}

Divide the numbers:

\frac{50}{50} = 1

= sin (\frac{θ}{2})

Simplify

\frac{\frac{3}{2}}{50} : \frac{3}{100}

\frac{\frac{3}{2}}{50}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{3}{2 \cdot 50}

Multiply the numbers:

2 \cdot 50 = 100

= \frac{3}{100}

sin (\frac{θ}{2}) = \frac{3}{100}

sin (\frac{θ}{2}) = \frac{3}{100}

sin (\frac{θ}{2}) = \frac{3}{100}

Apply trig inverse properties

sin (\frac{θ}{2}) = \frac{3}{100}

General solutions for

sin (\frac{θ}{2}) = \frac{3}{100}

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

\frac{θ}{2} = arcsin (\frac{3}{100}) + 2 πn, \frac{θ}{2} = π - arcsin (\frac{3}{100}) + 2 πn

\frac{θ}{2} = arcsin (\frac{3}{100}) + 2 πn, \frac{θ}{2} = π - arcsin (\frac{3}{100}) + 2 πn

Solve

\frac{θ}{2} = arcsin (\frac{3}{100}) + 2 πn : θ = 2 arcsin (\frac{3}{100}) + 4 πn

\frac{θ}{2} = arcsin (\frac{3}{100}) + 2 πn

Multiply both sides by

2

\frac{θ}{2} = arcsin (\frac{3}{100}) + 2 πn

Multiply both sides by

2

\frac{2 θ}{2} = 2 arcsin (\frac{3}{100}) + 2 \cdot 2 πn

Simplify

\frac{2 θ}{2} = 2 arcsin (\frac{3}{100}) + 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{3}{100}) + 2 \cdot 2 πn : 2 arcsin (\frac{3}{100}) + 4 πn

2 arcsin (\frac{3}{100}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 arcsin (\frac{3}{100}) + 4 πn

θ = 2 arcsin (\frac{3}{100}) + 4 πn

θ = 2 arcsin (\frac{3}{100}) + 4 πn

θ = 2 arcsin (\frac{3}{100}) + 4 πn

Solve

\frac{θ}{2} = π - arcsin (\frac{3}{100}) + 2 πn : θ = 2 π - 2 arcsin (\frac{3}{100}) + 4 πn

\frac{θ}{2} = π - arcsin (\frac{3}{100}) + 2 πn

Multiply both sides by

2

\frac{θ}{2} = π - arcsin (\frac{3}{100}) + 2 πn

Multiply both sides by

2

\frac{2 θ}{2} = 2 π - 2 arcsin (\frac{3}{100}) + 2 \cdot 2 πn

Simplify

\frac{2 θ}{2} = 2 π - 2 arcsin (\frac{3}{100}) + 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{3}{100}) + 2 \cdot 2 πn : 2 π - 2 arcsin (\frac{3}{100}) + 4 πn

2 π - 2 arcsin (\frac{3}{100}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 π - 2 arcsin (\frac{3}{100}) + 4 πn

θ = 2 π - 2 arcsin (\frac{3}{100}) + 4 πn

θ = 2 π - 2 arcsin (\frac{3}{100}) + 4 πn

θ = 2 π - 2 arcsin (\frac{3}{100}) + 4 πn

θ = 2 arcsin (\frac{3}{100}) + 4 πn, θ = 2 π - 2 arcsin (\frac{3}{100}) + 4 πn

Show solutions in decimal form

θ = 2 \cdot 0.03000 \dots + 4 πn, θ = 2 π - 2 \cdot 0.03000 \dots + 4 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 3/2 =2*25sin(θ/2) ?
The general solution for 3/2 =2*25sin(θ/2) is θ=2*0.03000…+4pin,θ=2pi-2*0.03000…+4pin