What is the general solution for -9.81+5(32.17)(12/2)sin(θ)=0 ?

The general solution for -9.81+5(32.17)(12/2)sin(θ)=0 is θ=0.01016…+2pin,θ=pi-0.01016…+2pin

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-9.81+5(32.17)(12/2)sin(θ)=0

- 9.81 + 5 (32.17) (\frac{12}{2}) sin (θ) = 0

θ = 0.01016 \dots + 2 πn, θ = π - 0.01016 \dots + 2 πn

Degrees

θ = 0.58240 \dots^{\circ} + 36 0^{\circ} n, θ = 179.41759 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- 9.81 + 5 (32.17) (\frac{12}{2}) sin (θ) = 0

5 \cdot 32.17 \cdot \frac{12}{2} sin (θ) = 965.1 sin (θ)

5 \cdot 32.17 \cdot \frac{12}{2} sin (θ)

Multiply fractions:

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

= 32.17 \cdot \frac{12 \cdot 5 sin ( θ )}{2}

Simplify

\frac{12 \cdot 5 sin ( θ )}{2} : 30 sin (θ)

\frac{12 \cdot 5 sin ( θ )}{2}

Multiply the numbers:

12 \cdot 5 = 60

= \frac{60 sin ( θ )}{2}

Divide the numbers:

\frac{60}{2} = 30

= 30 sin (θ)

= 30 \cdot 32.17 sin (θ)

Multiply the numbers:

32.17 \cdot 30 = 965.1

= 965.1 sin (θ)

- 9.81 + 965.1 sin (θ) = 0

Multiply both sides by

100

- 9.81 + 965.1 sin (θ) = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

- 9.81 \cdot 100 + 965.1 sin (θ) \cdot 100 = 0 \cdot 100

Refine

- 981 + 96510 sin (θ) = 0

- 981 + 96510 sin (θ) = 0

Move

981

to the right side

- 981 + 96510 sin (θ) = 0

Add

981

to both sides

- 981 + 96510 sin (θ) + 981 = 0 + 981

Simplify

96510 sin (θ) = 981

96510 sin (θ) = 981

Divide both sides by

96510

96510 sin (θ) = 981

Divide both sides by

96510

\frac{96510 sin ( θ )}{96510} = \frac{981}{96510}

Simplify

sin (θ) = \frac{327}{32170}

sin (θ) = \frac{327}{32170}

Apply trig inverse properties

sin (θ) = \frac{327}{32170}

General solutions for

sin (θ) = \frac{327}{32170}

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

θ = arcsin (\frac{327}{32170}) + 2 πn, θ = π - arcsin (\frac{327}{32170}) + 2 πn

θ = arcsin (\frac{327}{32170}) + 2 πn, θ = π - arcsin (\frac{327}{32170}) + 2 πn

Show solutions in decimal form

θ = 0.01016 \dots + 2 πn, θ = π - 0.01016 \dots + 2 πn

2 sin^{3} (x) - sin^{2} (x) - 2 sin (x) + 1 = 0

2 sin (x) = - 2

3 sin (x) = sin (x) + 1

sin (4 x) = sin (x)

3 sin (2 θ) - 4 sin (θ) = 0

What is the general solution for -9.81+5(32.17)(12/2)sin(θ)=0 ?
The general solution for -9.81+5(32.17)(12/2)sin(θ)=0 is θ=0.01016…+2pin,θ=pi-0.01016…+2pin