What is the general solution for sin(θ)=(150N)/(212.6N)(0.9063) ?

The general solution for sin(θ)=(150N)/(212.6N)(0.9063) is θ=0.69377…+2pin,θ=pi-0.69377…+2pin

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sin(θ)=(150N)/(212.6N)(0.9063)

sin (θ) = \frac{150 N}{212.6 N} (0.9063)

θ = 0.69377 \dots + 2 πn, θ = π - 0.69377 \dots + 2 πn

Radians

θ = 0.69377 \dots + 6.28318 \dots n, θ = π - 0.69377 \dots + 6.28318 \dots n

Solution steps

sin (θ) = \frac{150 N}{212.6 N} (0.9063)

Simplify

\frac{150 N}{212.6 N} \cdot 0.9063 : \frac{135.945}{212.6}

\frac{150 N}{212.6 N} \cdot 0.9063

\frac{150 N}{212.6 N} = \frac{150}{212.6}

\frac{150 N}{212.6 N}

Cancel the common factor:

N

= \frac{150}{212.6}

= 0.9063 \cdot \frac{150}{212.6}

Multiply fractions:

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

= \frac{150 \cdot 0.9063}{212.6}

Multiply the numbers:

150 \cdot 0.9063 = 135.945

= \frac{135.945}{212.6}

Apply trig inverse properties

sin (θ) = \frac{135.945}{212.6}

General solutions for

sin (θ) = \frac{135.945}{212.6}

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

θ = arcsin (\frac{135.945}{212.6}) + 2 πn, θ = π - arcsin (\frac{135.945}{212.6}) + 2 πn

θ = arcsin (\frac{135.945}{212.6}) + 2 πn, θ = π - arcsin (\frac{135.945}{212.6}) + 2 πn

Show solutions in decimal form

θ = 0.69377 \dots + 2 πn, θ = π - 0.69377 \dots + 2 πn

3 sin (x) + 4 = 5 cos (x), [0.2 π]

sin (x + \frac{π}{6}) = 0

7 sin (x) + 3 = sin (x) + 2

24 cos (x) = 122

cos (3 x) = \frac{3}{3}

What is the general solution for sin(θ)=(150N)/(212.6N)(0.9063) ?
The general solution for sin(θ)=(150N)/(212.6N)(0.9063) is θ=0.69377…+2pin,θ=pi-0.69377…+2pin