What is the general solution for 1.65*sin(30)=1.33*sin(x) ?

The general solution for 1.65*sin(30)=1.33*sin(x) is x=0.66912…+360n,x=180-0.66912…+360n

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1.65sin(30)=1.33sin(x)

1.65 \cdot sin (3 0^{\circ}) = 1.33 \cdot sin (x)

x = 0.66912 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.66912 \dots + 36 0^{\circ} n

Solution steps

1.65 sin (3 0^{\circ}) = 1.33 sin (x)

sin (3 0^{\circ}) = \frac{1}{2}

1.65 \cdot \frac{1}{2} = 1.33 sin (x)

Switch sides

1.33 sin (x) = 1.65 \cdot \frac{1}{2}

Divide both sides by

1.33

sin (x) = 0.62030 \dots

Apply trig inverse properties

x = arcsin (0.62030 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.62030 \dots) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.66912 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.66912 \dots + 36 0^{\circ} n

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

cos (2 x) - sin (x) = 0.5

cos (θ) - 2 sin^{2} (θ) = - 1

4 + 4 cos (θ) = 0

- cot (2 θ) = 0

What is the general solution for 1.65*sin(30)=1.33*sin(x) ?
The general solution for 1.65*sin(30)=1.33*sin(x) is x=0.66912…+360n,x=180-0.66912…+360n