What is the general solution for (30)/(sin(90))=(30)/(sin(x)),x ?

The general solution for (30)/(sin(90))=(30)/(sin(x)),x is No Solution for x\in\mathbb{R}

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Popular Trigonometry >

(30)/(sin(90))=(30)/(sin(x)),x

Solution

\frac{30}{sin ( 9 0 ^{\circ} )} = \frac{30}{sin ( x )}, x

Solution

No Solution for x \in R

Solution steps

\frac{30}{sin ( 9 0 ^{\circ} )} = \frac{30}{sin ( x )}, x

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{30}{1} = \frac{30}{sin ( x )}

Cross multiply

\frac{30}{1} = \frac{30}{sin ( x )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

30 sin (x) = 1 \cdot 30

Simplify

1 \cdot 30 : 30

1 \cdot 30

Multiply the numbers:

1 \cdot 30 = 30

= 30

30 sin (x) = 30

30 sin (x) = 30

Divide both sides by

30

30 sin (x) = 30

Divide both sides by

30

\frac{30 sin ( x )}{30} = \frac{30}{30}

Simplify

sin (x) = 1

sin (x) = 1

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{30}{sin ( x )}

and compare to zero

sin (x) = 0

The following points are undefined

sin (x) = 0

Combine undefined points with solutions:

sin (x) = 1

General solutions for

sin (x) = 1

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}

x = 9 0^{\circ} + 36 0^{\circ} n

x = 9 0^{\circ} + 36 0^{\circ} n

Solutions for the range

x

No Solution for x \in R

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for (30)/(sin(90))=(30)/(sin(x)),x ?
The general solution for (30)/(sin(90))=(30)/(sin(x)),x is No Solution for x\in\mathbb{R}