What is the general solution for 1.0003sin(30)=1.46sin(x) ?

The general solution for 1.0003sin(30)=1.46sin(x) is x=0.34964…+360n,x=180-0.34964…+360n

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1.0003sin(30)=1.46sin(x)

1.0003 sin (3 0^{\circ}) = 1.46 sin (x)

x = 0.34964 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.34964 \dots + 36 0^{\circ} n

Solution steps

1.0003 sin (3 0^{\circ}) = 1.46 sin (x)

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

1.0003 \cdot \frac{1}{2} = 1.46 sin (x)

Switch sides

1.46 sin (x) = 1.0003 \cdot \frac{1}{2}

Divide both sides by

1.46

sin (x) = \frac{1.0003}{2.92}

Apply trig inverse properties

x = arcsin (\frac{1.0003}{2.92}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{1.0003}{2.92}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.34964 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.34964 \dots + 36 0^{\circ} n

3 tan (x) + 2 cos (x) = 0

(cos (x)) (b sin (x) - a) = 0, 0 \leq x < 2 π

cos (x) = - \frac{5}{34}

sin (3 x) = \frac{1}{2}, 0 \leq x \leq 1

sec (θ) = - \frac{1}{2}

What is the general solution for 1.0003sin(30)=1.46sin(x) ?
The general solution for 1.0003sin(30)=1.46sin(x) is x=0.34964…+360n,x=180-0.34964…+360n