What is the general solution for sin(θ)=(20N)/(35N) ?

The general solution for sin(θ)=(20N)/(35N) is θ=0.60824…+2pin,θ=pi-0.60824…+2pin

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sin(θ)=(20N)/(35N)

sin (θ) = \frac{20 N}{35 N}

θ = 0.60824 \dots + 2 πn, θ = π - 0.60824 \dots + 2 πn

Radians

θ = 0.60824 \dots + 6.28318 \dots n, θ = π - 0.60824 \dots + 6.28318 \dots n

Solution steps

sin (θ) = \frac{20 N}{35 N}

Simplify

\frac{20 N}{35 N} : \frac{4}{7}

\frac{20 N}{35 N}

Cancel the common factor:

5

= \frac{4 N}{7 N}

Cancel the common factor:

N

= \frac{4}{7}

Apply trig inverse properties

sin (θ) = \frac{4}{7}

General solutions for

sin (θ) = \frac{4}{7}

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

θ = arcsin (\frac{4}{7}) + 2 πn, θ = π - arcsin (\frac{4}{7}) + 2 πn

θ = arcsin (\frac{4}{7}) + 2 πn, θ = π - arcsin (\frac{4}{7}) + 2 πn

Show solutions in decimal form

θ = 0.60824 \dots + 2 πn, θ = π - 0.60824 \dots + 2 πn

22 sin (θ) + 2 = 0

2 sin (2 θ) = 2 cos (θ)

1 + 3 tan (\frac{2 x - π}{3}) = 0

tan (3 x) = tan (π x)

sin^{2} (2 x) = 0.5

What is the general solution for sin(θ)=(20N)/(35N) ?
The general solution for sin(θ)=(20N)/(35N) is θ=0.60824…+2pin,θ=pi-0.60824…+2pin