What is the general solution for (1)sin(50)=(sqrt(6))sin(θ) ?

The general solution for (1)sin(50)=(sqrt(6))sin(θ) is θ=0.31807…+360n,θ=180-0.31807…+360n

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(1)sin(50)=(sqrt(6))sin(θ)

(1) sin (5 0^{\circ}) = (6) sin (θ)

θ = 0.31807 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.31807 \dots + 36 0^{\circ} n

Radians

θ = 0.31807 \dots + 2 πn, θ = π - 0.31807 \dots + 2 πn

Solution steps

(1) sin (5 0^{\circ}) = (6) sin (θ)

Switch sides

6 sin (θ) = 1 \cdot sin (5 0^{\circ})

Multiply:

1 \cdot sin (5 0^{\circ}) = sin (5 0^{\circ})

6 sin (θ) = sin (5 0^{\circ})

Divide both sides by

6

6 sin (θ) = sin (5 0^{\circ})

Divide both sides by

6

\frac{6 sin ( θ )}{6} = \frac{sin ( 5 0 ^{\circ} )}{6}

Simplify

\frac{6 sin ( θ )}{6} = \frac{sin ( 5 0 ^{\circ} )}{6}

Simplify

\frac{6 sin ( θ )}{6} : sin (θ)

\frac{6 sin ( θ )}{6}

Cancel the common factor:

6

= sin (θ)

Simplify

\frac{sin ( 5 0 ^{\circ} )}{6} : \frac{6 sin ( 5 0 ^{\circ} )}{6}

\frac{sin ( 5 0 ^{\circ} )}{6}

Multiply by the conjugate

\frac{6}{6}

= \frac{sin ( 5 0 ^{\circ} ) 6}{6 6}

66 = 6

66

Apply radical rule:

a a = a

66 = 6

= 6

= \frac{6 sin ( 5 0 ^{\circ} )}{6}

sin (θ) = \frac{6 sin ( 5 0 ^{\circ} )}{6}

sin (θ) = \frac{6 sin ( 5 0 ^{\circ} )}{6}

sin (θ) = \frac{6 sin ( 5 0 ^{\circ} )}{6}

Apply trig inverse properties

sin (θ) = \frac{6 sin ( 5 0 ^{\circ} )}{6}

General solutions for

sin (θ) = \frac{6 sin ( 5 0 ^{\circ} )}{6}

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

θ = arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{6}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{6}) + 36 0^{\circ} n

θ = arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{6}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{6}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.31807 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.31807 \dots + 36 0^{\circ} n

cos (2 x - 3 0^{\circ}) = 0

sin (5 a) = 0

x, y = 2 sin (x y)

tan (x) cos (x) sin (x) - 1 = 0

sin (2 x) + 3 cos^{2} (x) sin (x) = 0

What is the general solution for (1)sin(50)=(sqrt(6))sin(θ) ?
The general solution for (1)sin(50)=(sqrt(6))sin(θ) is θ=0.31807…+360n,θ=180-0.31807…+360n