What is the general solution for 2/3 =(sin(x))/(sin(135)) ?

The general solution for 2/3 =(sin(x))/(sin(135)) is x=0.49088…+360n,x=180-0.49088…+360n

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2/3 =(sin(x))/(sin(135))

\frac{2}{3} = \frac{sin ( x )}{sin ( 13 5 ^{\circ} )}

x = 0.49088 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.49088 \dots + 36 0^{\circ} n

Solution steps

\frac{2}{3} = \frac{sin ( x )}{sin ( 13 5 ^{\circ} )}

Switch sides

\frac{sin ( x )}{sin ( 13 5 ^{\circ} )} = \frac{2}{3}

sin (13 5^{\circ}) = \frac{2}{2}

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

Multiply both sides by

\frac{2}{2}

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

Apply trig inverse properties

x = arcsin (\frac{2}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2}{3}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.49088 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.49088 \dots + 36 0^{\circ} n

sin (x) + 2 (cos (x))^{2} = 1

a sin (2 θ) = 0

cos (2 x) = 0, x \leq 2 π, 0

7 + csc (2 x) = 3 cot^{2} (2 x)

cos (θ) = cos (\frac{π}{13})

What is the general solution for 2/3 =(sin(x))/(sin(135)) ?
The general solution for 2/3 =(sin(x))/(sin(135)) is x=0.49088…+360n,x=180-0.49088…+360n