What is the general solution for (0.866)/(sin(x))=1.53 ?

The general solution for (0.866)/(sin(x))=1.53 is x=0.60166…+2pin,x=pi-0.60166…+2pin

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(0.866)/(sin(x))=1.53

\frac{0.866}{sin ( x )} = 1.53

x = 0.60166 \dots + 2 πn, x = π - 0.60166 \dots + 2 πn

Degrees

x = 34.47267 \dots^{\circ} + 36 0^{\circ} n, x = 145.52732 \dots^{\circ} + 36 0^{\circ} n

Solution steps

\frac{0.866}{sin ( x )} = 1.53

Multiply both sides by

sin (x)

\frac{0.866}{sin ( x )} = 1.53

Multiply both sides by

sin (x)

\frac{0.866}{sin ( x )} sin (x) = 1.53 sin (x)

Simplify

0.866 = 1.53 sin (x)

0.866 = 1.53 sin (x)

Switch sides

1.53 sin (x) = 0.866

Multiply both sides by

1000

1.53 sin (x) = 0.866

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

1.53 sin (x) \cdot 1000 = 0.866 \cdot 1000

Refine

1530 sin (x) = 866

1530 sin (x) = 866

Divide both sides by

1530

1530 sin (x) = 866

Divide both sides by

1530

\frac{1530 sin ( x )}{1530} = \frac{866}{1530}

Simplify

sin (x) = \frac{433}{765}

sin (x) = \frac{433}{765}

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{0.866}{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{433}{765}

Apply trig inverse properties

sin (x) = \frac{433}{765}

General solutions for

sin (x) = \frac{433}{765}

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

x = arcsin (\frac{433}{765}) + 2 πn, x = π - arcsin (\frac{433}{765}) + 2 πn

x = arcsin (\frac{433}{765}) + 2 πn, x = π - arcsin (\frac{433}{765}) + 2 πn

Show solutions in decimal form

x = 0.60166 \dots + 2 πn, x = π - 0.60166 \dots + 2 πn

3 sin (2 x) + 1 = 2

2 cos^{4} (x) - 2 cos^{2} (x) = 4 cos^{2} (x) - 1

x, t^{2} = 2 sec (x)

(8 cos (x) - 4) (sin (x)) = 0, 0 \leq x < 2 π

sin (x) = 3511

What is the general solution for (0.866)/(sin(x))=1.53 ?
The general solution for (0.866)/(sin(x))=1.53 is x=0.60166…+2pin,x=pi-0.60166…+2pin