What is the general solution for (sin(40))/8 =(sin(65.38))/(sin(x)) ?

The general solution for (sin(40))/8 =(sin(65.38))/(sin(x)) is No Solution for x\in\mathbb{R}

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(sin(40))/8 =(sin(65.38))/(sin(x))

\frac{sin ( 4 0 ^{\circ} )}{8} = \frac{sin ( 65.3 8 ^{\circ} )}{sin ( x )}

No Solution for x \in R

Solution steps

\frac{sin ( 4 0 ^{\circ} )}{8} = \frac{sin ( 65.3 8 ^{\circ} )}{sin ( x )}

Cross multiply

\frac{sin ( 4 0 ^{\circ} )}{8} = \frac{sin ( 65.3 8 ^{\circ} )}{sin ( x )}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

sin (4 0^{\circ}) sin (x) = 8 sin (65.3 8^{\circ})

sin (4 0^{\circ}) sin (x) = 8 sin (65.3 8^{\circ})

Divide both sides by

sin (4 0^{\circ})

sin (4 0^{\circ}) sin (x) = 8 sin (65.3 8^{\circ})

Divide both sides by

sin (4 0^{\circ})

\frac{sin ( 4 0 ^{\circ} ) sin ( x )}{sin ( 4 0 ^{\circ} )} = \frac{8 sin ( 65.3 8 ^{\circ} )}{sin ( 4 0 ^{\circ} )}

Simplify

sin (x) = \frac{8 sin ( 65.3 8 ^{\circ} )}{sin ( 4 0 ^{\circ} )}

sin (x) = \frac{8 sin ( 65.3 8 ^{\circ} )}{sin ( 4 0 ^{\circ} )}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{sin ( 65.3 8 ^{\circ} )}{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{8 sin ( 65.3 8 ^{\circ} )}{sin ( 4 0 ^{\circ} )}

- 1 \leq sin (x) \leq 1

No Solution for x \in R

cos (28 π + x) = \frac{1}{2}

1 - tan^{2} (x) = \frac{cos ^{2} ( x )}{cos ^{2} ( x )}

- 2 = - 2 sec (x) + tan^{2} (x)

tan^{2} (y) + 1 = cos^{2} (y)

4 sin (2 x) + csc (2 x) = 4

What is the general solution for (sin(40))/8 =(sin(65.38))/(sin(x)) ?
The general solution for (sin(40))/8 =(sin(65.38))/(sin(x)) is No Solution for x\in\mathbb{R}