What is the general solution for 2/3 =(sin(135))/(sin(x)) ?

The general solution for 2/3 =(sin(135))/(sin(x)) is No Solution for x\in\mathbb{R}

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Popular Trigonometry >

2/3 =(sin(135))/(sin(x))

Solution

\frac{2}{3} = \frac{sin ( 13 5 ^{\circ} )}{sin ( x )}

Solution

No Solution for x \in R

Solution steps

\frac{2}{3} = \frac{sin ( 13 5 ^{\circ} )}{sin ( x )}

Switch sides

\frac{sin ( 13 5 ^{\circ} )}{sin ( x )} = \frac{2}{3}

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\circ})

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\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}

= \frac{2}{2}

= \frac{2}{2}

\frac{\frac{2}{2}}{sin ( x )} = \frac{2}{3}

Cross multiply

\frac{\frac{2}{2}}{sin ( x )} = \frac{2}{3}

Simplify

\frac{\frac{2}{2}}{sin ( x )} : \frac{2}{2 sin ( x )}

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

Apply the fraction rule:

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

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

\frac{2}{2 sin ( x )} = \frac{2}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

2 \cdot 3 = 2 sin (x) \cdot 2

Simplify

2 sin (x) \cdot 2 : 4 sin (x)

2 sin (x) \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4 sin (x)

2 \cdot 3 = 4 sin (x)

2 \cdot 3 = 4 sin (x)

Switch sides

4 sin (x) = 2 \cdot 3

Divide both sides by

4

4 sin (x) = 2 \cdot 3

Divide both sides by

4

\frac{4 sin ( x )}{4} = \frac{2 \cdot 3}{4}

Simplify

sin (x) = \frac{2 \cdot 3}{4}

sin (x) = \frac{2 \cdot 3}{4}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

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

and compare to zero

sin (x) = 0

The following points are undefined

sin (x) = 0

Combine undefined points with solutions:

sin (x) = \frac{2 \cdot 3}{4}

- 1 \leq sin (x) \leq 1

No Solution for x \in R

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 2/3 =(sin(135))/(sin(x)) ?
The general solution for 2/3 =(sin(135))/(sin(x)) is No Solution for x\in\mathbb{R}