What is the general solution for (sin(x))/(120)=(sin(60))/(300) ?

The general solution for (sin(x))/(120)=(sin(60))/(300) is x=0.35374…+360n,x=180-0.35374…+360n

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Popular >

(sin(x))/(120)=(sin(60))/(300)

Solution

\frac{sin ( x )}{120} = \frac{sin ( 6 0 ^{\circ} )}{300}

Solution

x = 0.35374 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.35374 \dots + 36 0^{\circ} n

Radians

x = 0.35374 \dots + 2 πn, x = π - 0.35374 \dots + 2 πn

Solution steps

\frac{sin ( x )}{120} = \frac{sin ( 6 0 ^{\circ} )}{300}

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

= \frac{3}{2}

\frac{sin ( x )}{120} = \frac{\frac{3}{2}}{300}

Multiply both sides by

100

\frac{sin ( x )}{120} = \frac{\frac{3}{2}}{300}

Multiply both sides by

100

\frac{sin ( x )}{120} \cdot 100 = \frac{\frac{3}{2}}{300} \cdot 100

Simplify

\frac{sin ( x )}{120} \cdot 100 = \frac{\frac{3}{2}}{300} \cdot 100

Simplify

\frac{sin ( x )}{120} \cdot 100 : \frac{5 sin ( x )}{6}

\frac{sin ( x )}{120} \cdot 100

Multiply fractions:

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

= \frac{sin ( x ) \cdot 100}{120}

Cancel the common factor:

20

= \frac{5 sin ( x )}{6}

Simplify

\frac{\frac{3}{2}}{300} \cdot 100 : \frac{3}{6}

\frac{\frac{3}{2}}{300} \cdot 100

\frac{\frac{3}{2}}{300} = \frac{3}{600}

\frac{\frac{3}{2}}{300}

Apply the fraction rule:

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

= \frac{3}{2 \cdot 300}

Multiply the numbers:

2 \cdot 300 = 600

= \frac{3}{600}

= 100 \cdot \frac{3}{600}

Multiply fractions:

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

= \frac{3 \cdot 100}{600}

Cancel the common factor:

100

= \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

Multiply both sides by

6

\frac{5 sin ( x )}{6} = \frac{3}{6}

Multiply both sides by

6

\frac{6 \cdot 5 sin ( x )}{6} = \frac{6 3}{6}

Simplify

5 sin (x) = 3

5 sin (x) = 3

Divide both sides by

5

5 sin (x) = 3

Divide both sides by

5

\frac{5 sin ( x )}{5} = \frac{3}{5}

Simplify

sin (x) = \frac{3}{5}

sin (x) = \frac{3}{5}

Apply trig inverse properties

sin (x) = \frac{3}{5}

General solutions for

sin (x) = \frac{3}{5}

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

x = arcsin (\frac{3}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{5}) + 36 0^{\circ} n

x = arcsin (\frac{3}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{5}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.35374 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.35374 \dots + 36 0^{\circ} n

Popular Examples

8sin(θ)+15cos(θ)=0

8 sin (θ) + 15 cos (θ) = 0

sin(t)= 3/7

sin (t) = \frac{3}{7}

cos(2x-1)=sin(3x+6)

cos (2 x - 1) = sin (3 x + 6)

(sin(b))/(300)=(sin(49))/(500)

\frac{sin ( b )}{300} = \frac{sin ( 4 9 ^{\circ} )}{500}

sin(θ)=cos(2θ+60)

sin (θ) = cos (2 θ + 6 0^{\circ})

Frequently Asked Questions (FAQ)

What is the general solution for (sin(x))/(120)=(sin(60))/(300) ?
The general solution for (sin(x))/(120)=(sin(60))/(300) is x=0.35374…+360n,x=180-0.35374…+360n