What is the general solution for 589*sin(45)=443*sin(x) ?

The general solution for 589*sin(45)=443*sin(x) is x=1.22306…+360n,x=180-1.22306…+360n

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589sin(45)=443sin(x)

589 \cdot sin (4 5^{\circ}) = 443 \cdot sin (x)

x = 1.22306 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.22306 \dots + 36 0^{\circ} n

Solution steps

589 sin (4 5^{\circ}) = 443 sin (x)

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

589 \cdot \frac{2}{2} = 443 sin (x)

Switch sides

443 sin (x) = 589 \cdot \frac{2}{2}

Divide both sides by

443

sin (x) = \frac{589 2}{886}

Apply trig inverse properties

x = arcsin (\frac{589 2}{886}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{589 2}{886}) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.22306 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.22306 \dots + 36 0^{\circ} n

cos (θ) = 0.7609

sin (x) = \frac{3}{2}, 0 \leq x < 2 π

cos (8 x) \cdot 8 = 0

\frac{13}{12} = cosh (\frac{x}{120})

θ, r = - \frac{3}{r cos ( θ )}

What is the general solution for 589*sin(45)=443*sin(x) ?
The general solution for 589*sin(45)=443*sin(x) is x=1.22306…+360n,x=180-1.22306…+360n