What is the general solution for (sin(60))/(174.36)=(sin(x))/(200) ?

The general solution for (sin(60))/(174.36)=(sin(x))/(200) is x=1.45563…+360n,x=180-1.45563…+360n

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Popular Trigonometry >

(sin(60))/(174.36)=(sin(x))/(200)

Solution

\frac{sin ( 6 0 ^{\circ} )}{174.36} = \frac{sin ( x )}{200}

Solution

x = 1.45563 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.45563 \dots + 36 0^{\circ} n

Radians

x = 1.45563 \dots + 2 πn, x = π - 1.45563 \dots + 2 πn

Solution steps

\frac{sin ( 6 0 ^{\circ} )}{174.36} = \frac{sin ( x )}{200}

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{\frac{3}{2}}{174.36} = \frac{sin ( x )}{200}

Switch sides

\frac{sin ( x )}{200} = \frac{\frac{3}{2}}{174.36}

Multiply both sides by

100

\frac{sin ( x )}{200} = \frac{\frac{3}{2}}{174.36}

Multiply both sides by

100

\frac{sin ( x )}{200} \cdot 100 = \frac{\frac{3}{2}}{174.36} \cdot 100

Simplify

\frac{sin ( x )}{200} \cdot 100 = \frac{\frac{3}{2}}{174.36} \cdot 100

Simplify

\frac{sin ( x )}{200} \cdot 100 : \frac{sin ( x )}{2}

\frac{sin ( x )}{200} \cdot 100

Multiply fractions:

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

= \frac{sin ( x ) \cdot 100}{200}

Cancel the common factor:

100

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

Simplify

\frac{\frac{3}{2}}{174.36} \cdot 100 : \frac{100 3}{348.72}

\frac{\frac{3}{2}}{174.36} \cdot 100

\frac{\frac{3}{2}}{174.36} = \frac{3}{348.72}

\frac{\frac{3}{2}}{174.36}

Apply the fraction rule:

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

= \frac{3}{2 \cdot 174.36}

Multiply the numbers:

2 \cdot 174.36 = 348.72

= \frac{3}{348.72}

= 100 \cdot \frac{3}{348.72}

Multiply fractions:

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

= \frac{3 \cdot 100}{348.72}

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

Multiply both sides by

2

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

Multiply both sides by

2

\frac{2 sin ( x )}{2} = \frac{2 \cdot 100 3}{348.72}

Simplify

\frac{2 sin ( x )}{2} = \frac{2 \cdot 100 3}{348.72}

Simplify

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

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

Divide the numbers:

\frac{2}{2} = 1

= sin (x)

Simplify

\frac{2 \cdot 100 3}{348.72} : 0.99337 \dots

\frac{2 \cdot 100 3}{348.72}

Multiply the numbers:

2 \cdot 100 = 200

= \frac{200 3}{348.72}

Convert element to a decimal form

3 = 1.73205 \dots

= \frac{200 \cdot 1.73205 \dots}{348.72}

Multiply the numbers:

200 \cdot 1.73205 \dots = 346.41016 \dots

= \frac{346.41016 \dots}{348.72}

Divide the numbers:

\frac{346.41016 \dots}{348.72} = 0.99337 \dots

= 0.99337 \dots

sin (x) = 0.99337 \dots

sin (x) = 0.99337 \dots

sin (x) = 0.99337 \dots

Apply trig inverse properties

sin (x) = 0.99337 \dots

General solutions for

sin (x) = 0.99337 \dots

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

x = arcsin (0.99337 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.99337 \dots) + 36 0^{\circ} n

x = arcsin (0.99337 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.99337 \dots) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.45563 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.45563 \dots + 36 0^{\circ} n

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for (sin(60))/(174.36)=(sin(x))/(200) ?
The general solution for (sin(60))/(174.36)=(sin(x))/(200) is x=1.45563…+360n,x=180-1.45563…+360n