What is the general solution for 3.25=(9.8)sin(θ) ?

The general solution for 3.25=(9.8)sin(θ) is θ=0.33803…+2pin,θ=pi-0.33803…+2pin

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3.25=(9.8)sin(θ)

3.25 = (9.8) sin (θ)

θ = 0.33803 \dots + 2 πn, θ = π - 0.33803 \dots + 2 πn

Degrees

θ = 19.36790 \dots^{\circ} + 36 0^{\circ} n, θ = 160.63209 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3.25 = (9.8) sin (θ)

Switch sides

9.8 sin (θ) = 3.25

Multiply both sides by

100

9.8 sin (θ) = 3.25

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

9.8 sin (θ) \cdot 100 = 3.25 \cdot 100

Refine

980 sin (θ) = 325

980 sin (θ) = 325

Divide both sides by

980

980 sin (θ) = 325

Divide both sides by

980

\frac{980 sin ( θ )}{980} = \frac{325}{980}

Simplify

sin (θ) = \frac{65}{196}

sin (θ) = \frac{65}{196}

Apply trig inverse properties

sin (θ) = \frac{65}{196}

General solutions for

sin (θ) = \frac{65}{196}

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

θ = arcsin (\frac{65}{196}) + 2 πn, θ = π - arcsin (\frac{65}{196}) + 2 πn

θ = arcsin (\frac{65}{196}) + 2 πn, θ = π - arcsin (\frac{65}{196}) + 2 πn

Show solutions in decimal form

θ = 0.33803 \dots + 2 πn, θ = π - 0.33803 \dots + 2 πn

sin (θ) = - 3

sin (3 x - \frac{π}{3}) = \frac{1}{2}

- cos (θ) + cos (2 θ) = 0

cos (x) (cos (x) + 1) = 0

3 = 6 sin (θ)

What is the general solution for 3.25=(9.8)sin(θ) ?
The general solution for 3.25=(9.8)sin(θ) is θ=0.33803…+2pin,θ=pi-0.33803…+2pin