What is the general solution for (700)/(sin(90))=(236.3277)/(sin(θ)) ?

The general solution for (700)/(sin(90))=(236.3277)/(sin(θ)) is θ=0.34437…+360n,θ=180-0.34437…+360n

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(700)/(sin(90))=(236.3277)/(sin(θ))

\frac{700}{sin ( 9 0 ^{\circ} )} = \frac{236.3277}{sin ( θ )}

θ = 0.34437 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.34437 \dots + 36 0^{\circ} n

Radians

θ = 0.34437 \dots + 2 πn, θ = π - 0.34437 \dots + 2 πn

Solution steps

\frac{700}{sin ( 9 0 ^{\circ} )} = \frac{236.3277}{sin ( θ )}

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

Use the following trivial identity:

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1

\frac{700}{1} = \frac{236.3277}{sin ( θ )}

Cross multiply

\frac{700}{1} = \frac{236.3277}{sin ( θ )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

700 sin (θ) = 1 \cdot 236.3277

Simplify

1 \cdot 236.3277 : 236.3277

1 \cdot 236.3277

Multiply the numbers:

1 \cdot 236.3277 = 236.3277

= 236.3277

700 sin (θ) = 236.3277

700 sin (θ) = 236.3277

Divide both sides by

700

700 sin (θ) = 236.3277

Divide both sides by

700

\frac{700 sin ( θ )}{700} = \frac{236.3277}{700}

Simplify

sin (θ) = \frac{236.3277}{700}

sin (θ) = \frac{236.3277}{700}

Verify Solutions

Find undefined (singularity) points:

sin (θ) = 0

Take the denominator(s) of

\frac{236.3277}{sin ( θ )}

and compare to zero

sin (θ) = 0

The following points are undefined

sin (θ) = 0

Combine undefined points with solutions:

sin (θ) = \frac{236.3277}{700}

Apply trig inverse properties

sin (θ) = \frac{236.3277}{700}

General solutions for

sin (θ) = \frac{236.3277}{700}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

θ = arcsin (\frac{236.3277}{700}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{236.3277}{700}) + 36 0^{\circ} n

θ = arcsin (\frac{236.3277}{700}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{236.3277}{700}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.34437 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.34437 \dots + 36 0^{\circ} n

cos (x) + cos (2 x) = - 0.75

x, 2 y = sin (2 x)

- csc (θ) + 5 = cot (θ) + 6

sin (θ) - 0.2 \cdot cos (θ) = 0.11836

2 sin^{2} (x) - 3 = cos (x) - 2

What is the general solution for (700)/(sin(90))=(236.3277)/(sin(θ)) ?
The general solution for (700)/(sin(90))=(236.3277)/(sin(θ)) is θ=0.34437…+360n,θ=180-0.34437…+360n