What is the general solution for (sin(θ))/(60)=(sin(45))/(246.26) ?

The general solution for (sin(θ))/(60)=(sin(45))/(246.26) is θ=0.17314…+360n,θ=180-0.17314…+360n

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Popular >

(sin(θ))/(60)=(sin(45))/(246.26)

Solution

\frac{sin ( θ )}{60} = \frac{sin ( 4 5 ^{\circ} )}{246.26}

Solution

θ = 0.17314 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.17314 \dots + 36 0^{\circ} n

Radians

θ = 0.17314 \dots + 2 πn, θ = π - 0.17314 \dots + 2 πn

Solution steps

\frac{sin ( θ )}{60} = \frac{sin ( 4 5 ^{\circ} )}{246.26}

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\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{2}{2}

= \frac{2}{2}

\frac{sin ( θ )}{60} = \frac{\frac{2}{2}}{246.26}

Multiply both sides by

10

\frac{sin ( θ )}{60} = \frac{\frac{2}{2}}{246.26}

Multiply both sides by

10

\frac{sin ( θ )}{60} \cdot 10 = \frac{\frac{2}{2}}{246.26} \cdot 10

Simplify

\frac{sin ( θ )}{60} \cdot 10 = \frac{\frac{2}{2}}{246.26} \cdot 10

Simplify

\frac{sin ( θ )}{60} \cdot 10 : \frac{sin ( θ )}{6}

\frac{sin ( θ )}{60} \cdot 10

Multiply fractions:

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

= \frac{sin ( θ ) \cdot 10}{60}

Cancel the common factor:

10

= \frac{sin ( θ )}{6}

Simplify

\frac{\frac{2}{2}}{246.26} \cdot 10 : \frac{10 2}{492.52}

\frac{\frac{2}{2}}{246.26} \cdot 10

\frac{\frac{2}{2}}{246.26} = \frac{2}{492.52}

\frac{\frac{2}{2}}{246.26}

Apply the fraction rule:

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

= \frac{2}{2 \cdot 246.26}

Multiply the numbers:

2 \cdot 246.26 = 492.52

= \frac{2}{492.52}

= 10 \cdot \frac{2}{492.52}

Multiply fractions:

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

= \frac{2 \cdot 10}{492.52}

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

Multiply both sides by

6

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

Multiply both sides by

6

\frac{6 sin ( θ )}{6} = \frac{6 \cdot 10 2}{492.52}

Simplify

\frac{6 sin ( θ )}{6} = \frac{6 \cdot 10 2}{492.52}

Simplify

\frac{6 sin ( θ )}{6} : sin (θ)

\frac{6 sin ( θ )}{6}

Divide the numbers:

\frac{6}{6} = 1

= sin (θ)

Simplify

\frac{6 \cdot 10 2}{492.52} : 0.17228 \dots

\frac{6 \cdot 10 2}{492.52}

Multiply the numbers:

6 \cdot 10 = 60

= \frac{60 2}{492.52}

Convert element to a decimal form

2 = 1.41421 \dots

= \frac{60 \cdot 1.41421 \dots}{492.52}

Multiply the numbers:

60 \cdot 1.41421 \dots = 84.85281 \dots

= \frac{84.85281 \dots}{492.52}

Divide the numbers:

\frac{84.85281 \dots}{492.52} = 0.17228 \dots

= 0.17228 \dots

sin (θ) = 0.17228 \dots

sin (θ) = 0.17228 \dots

sin (θ) = 0.17228 \dots

Apply trig inverse properties

sin (θ) = 0.17228 \dots

General solutions for

sin (θ) = 0.17228 \dots

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

θ = arcsin (0.17228 \dots) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (0.17228 \dots) + 36 0^{\circ} n

θ = arcsin (0.17228 \dots) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (0.17228 \dots) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.17314 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.17314 \dots + 36 0^{\circ} n

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Frequently Asked Questions (FAQ)

What is the general solution for (sin(θ))/(60)=(sin(45))/(246.26) ?
The general solution for (sin(θ))/(60)=(sin(45))/(246.26) is θ=0.17314…+360n,θ=180-0.17314…+360n