What is the general solution for 18= 1/2*9*5*sin(θ) ?

The general solution for 18= 1/2*9*5*sin(θ) is θ=0.92729…+2pin,θ=pi-0.92729…+2pin

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18= 1/295*sin(θ)

18 = \frac{1}{2} \cdot 9 \cdot 5 \cdot sin (θ)

θ = 0.92729 \dots + 2 πn, θ = π - 0.92729 \dots + 2 πn

Degrees

θ = 53.13010 \dots^{\circ} + 36 0^{\circ} n, θ = 126.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

18 = \frac{1}{2} \cdot 9 \cdot 5 sin (θ)

Switch sides

\frac{1}{2} \cdot 9 \cdot 5 sin (θ) = 18

Simplify

\frac{1}{2} \cdot 9 \cdot 5 : \frac{45}{2}

\frac{1}{2} \cdot 9 \cdot 5

Convert element to fraction:

9 = \frac{9}{1}

= 5 \cdot \frac{1}{2} \cdot \frac{9}{1}

Convert element to fraction:

5 = \frac{5}{1}

= \frac{1}{2} \cdot \frac{9}{1} \cdot \frac{5}{1}

Multiply fractions:

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

= \frac{1 \cdot 9 \cdot 5}{2 \cdot 1 \cdot 1}

Cancel the common factor:

1

= \frac{9 \cdot 5}{2 \cdot 1}

Multiply the numbers:

9 \cdot 5 = 45

= \frac{45}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{45}{2}

\frac{45}{2} sin (θ) = 18

Multiply both sides by

2

\frac{45}{2} sin (θ) = 18

Multiply both sides by

2

2 \cdot \frac{45}{2} sin (θ) = 18 \cdot 2

Simplify

45 sin (θ) = 36

45 sin (θ) = 36

Divide both sides by

45

45 sin (θ) = 36

Divide both sides by

45

\frac{45 sin ( θ )}{45} = \frac{36}{45}

Simplify

sin (θ) = \frac{4}{5}

sin (θ) = \frac{4}{5}

Apply trig inverse properties

sin (θ) = \frac{4}{5}

General solutions for

sin (θ) = \frac{4}{5}

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

θ = arcsin (\frac{4}{5}) + 2 πn, θ = π - arcsin (\frac{4}{5}) + 2 πn

θ = arcsin (\frac{4}{5}) + 2 πn, θ = π - arcsin (\frac{4}{5}) + 2 πn

Show solutions in decimal form

θ = 0.92729 \dots + 2 πn, θ = π - 0.92729 \dots + 2 πn

2 cos^{2} (x) = cos^{2} (x)

sin (\frac{π x}{2}) = 0

sin (x) = \frac{1}{2} 2

8 cos (2 x) = 2 sin (x) + 7

cos (θ) = 0.5332, θ

What is the general solution for 18= 1/2*9*5*sin(θ) ?
The general solution for 18= 1/2*9*5*sin(θ) is θ=0.92729…+2pin,θ=pi-0.92729…+2pin