What is the general solution for (sin(θ))/(60)=(sin(80))/(280.87) ?

The general solution for (sin(θ))/(60)=(sin(80))/(280.87) is θ=0.21196…+360n,θ=180-0.21196…+360n

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(sin(θ))/(60)=(sin(80))/(280.87)

\frac{sin ( θ )}{60} = \frac{sin ( 8 0 ^{\circ} )}{280.87}

θ = 0.21196 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.21196 \dots + 36 0^{\circ} n

Radians

θ = 0.21196 \dots + 2 πn, θ = π - 0.21196 \dots + 2 πn

Solution steps

\frac{sin ( θ )}{60} = \frac{sin ( 8 0 ^{\circ} )}{280.87}

Multiply both sides by

10

\frac{sin ( θ )}{60} = \frac{sin ( 8 0 ^{\circ} )}{280.87}

Multiply both sides by

10

\frac{sin ( θ )}{60} \cdot 10 = \frac{sin ( 8 0 ^{\circ} )}{280.87} \cdot 10

Simplify

\frac{sin ( θ )}{60} \cdot 10 = \frac{sin ( 8 0 ^{\circ} )}{280.87} \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{sin ( 8 0 ^{\circ} )}{280.87} \cdot 10 : \frac{10 sin ( 8 0 ^{\circ} )}{280.87}

\frac{sin ( 8 0 ^{\circ} )}{280.87} \cdot 10

Multiply fractions:

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

= \frac{sin ( 8 0 ^{\circ} ) \cdot 10}{280.87}

\frac{sin ( θ )}{6} = \frac{10 sin ( 8 0 ^{\circ} )}{280.87}

\frac{sin ( θ )}{6} = \frac{10 sin ( 8 0 ^{\circ} )}{280.87}

\frac{sin ( θ )}{6} = \frac{10 sin ( 8 0 ^{\circ} )}{280.87}

Multiply both sides by

6

\frac{sin ( θ )}{6} = \frac{10 sin ( 8 0 ^{\circ} )}{280.87}

Multiply both sides by

6

\frac{6 sin ( θ )}{6} = \frac{6 \cdot 10 sin ( 8 0 ^{\circ} )}{280.87}

Simplify

\frac{6 sin ( θ )}{6} = \frac{6 \cdot 10 sin ( 8 0 ^{\circ} )}{280.87}

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 sin ( 8 0 ^{\circ} )}{280.87} : \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

\frac{6 \cdot 10 sin ( 8 0 ^{\circ} )}{280.87}

Multiply the numbers:

6 \cdot 10 = 60

= \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

sin (θ) = \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

sin (θ) = \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

sin (θ) = \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

Apply trig inverse properties

sin (θ) = \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

General solutions for

sin (θ) = \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

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

θ = arcsin (\frac{60 sin ( 8 0 ^{\circ} )}{280.87}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{60 sin ( 8 0 ^{\circ} )}{280.87}) + 36 0^{\circ} n

θ = arcsin (\frac{60 sin ( 8 0 ^{\circ} )}{280.87}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{60 sin ( 8 0 ^{\circ} )}{280.87}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.21196 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.21196 \dots + 36 0^{\circ} n

What is the general solution for (sin(θ))/(60)=(sin(80))/(280.87) ?
The general solution for (sin(θ))/(60)=(sin(80))/(280.87) is θ=0.21196…+360n,θ=180-0.21196…+360n