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Popular >

1/(1.5)=(sin(30))/(sin(x)),x<90

Solution

\frac{1}{1.5} = \frac{sin ( 3 0 ^{\circ} )}{sin ( x )}, x < 9 0^{\circ}

Solution

x = 0.84806 \dots, x = - 5.43512 \dots, x = - 18 0^{\circ} - 0.84806 \dots, x = - 11.71830 \dots, x = - 10.27284 \dots, x = - 18.00149 \dots, x = - 16.55602 \dots, x = - 24.28467 \dots, x = - 22.83921 \dots

+1

Radians

x = 0.84806 \dots, x = - 5.43512 \dots, x = - π - 0.84806 \dots, x = - 11.71830 \dots, x = - 10.27284 \dots, x = - 18.00149 \dots, x = - 16.55602 \dots, x = - 24.28467 \dots, x = - 22.83921 \dots

Solution steps

\frac{1}{1.5} = \frac{sin ( 3 0 ^{\circ} )}{sin ( x )}, x < 9 0^{\circ}

Switch sides

\frac{sin ( 3 0 ^{\circ} )}{sin ( x )} = \frac{1}{1.5}

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 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}

= \frac{1}{2}

= \frac{1}{2}

\frac{\frac{1}{2}}{sin ( x )} = \frac{1}{1.5}

Cross multiply

\frac{\frac{1}{2}}{sin ( x )} = \frac{1}{1.5}

Simplify

\frac{\frac{1}{2}}{sin ( x )} : \frac{1}{2 sin ( x )}

\frac{\frac{1}{2}}{sin ( x )}

Apply the fraction rule:

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

= \frac{1}{2 sin ( x )}

\frac{1}{2 sin ( x )} = \frac{1}{1.5}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 1.5 = 2 sin (x) \cdot 1

Simplify

1 \cdot 1.5 = 2 sin (x) \cdot 1

Simplify

1 \cdot 1.5 : 1.5

1 \cdot 1.5

Multiply the numbers:

1 \cdot 1.5 = 1.5

= 1.5

Simplify

2 sin (x) \cdot 1 : 2 sin (x)

2 sin (x) \cdot 1

Multiply the numbers:

2 \cdot 1 = 2

= 2 sin (x)

1.5 = 2 sin (x)

1.5 = 2 sin (x)

1.5 = 2 sin (x)

Switch sides

2 sin (x) = 1.5

Divide both sides by

2

2 sin (x) = 1.5

Divide both sides by

2

\frac{2 sin ( x )}{2} = \frac{1.5}{2}

Simplify

sin (x) = 0.75

sin (x) = 0.75

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{\frac{1}{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) = 0.75

Apply trig inverse properties

sin (x) = 0.75

General solutions for

sin (x) = 0.75

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

x = arcsin (0.75) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.75) + 36 0^{\circ} n

x = arcsin (0.75) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.75) + 36 0^{\circ} n

Solutions for the range

x < 9 0^{\circ}

x = 0.84806 \dots, x = - 5.43512 \dots, x = - 18 0^{\circ} - 0.84806 \dots, x = - 11.71830 \dots, x = - 10.27284 \dots, x = - 18.00149 \dots, x = - 16.55602 \dots, x = - 24.28467 \dots, x = - 22.83921 \dots

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