What is the general solution for 1sin(30)=1.495sin(x) ?

The general solution for 1sin(30)=1.495sin(x) is x=0.34101…+360n,x=180-0.34101…+360n

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1sin(30)=1.495sin(x)

1 sin (3 0^{\circ}) = 1.495 sin (x)

x = 0.34101 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.34101 \dots + 36 0^{\circ} n

Radians

x = 0.34101 \dots + 2 πn, x = π - 0.34101 \dots + 2 πn

Solution steps

1 \cdot sin (3 0^{\circ}) = 1.495 sin (x)

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

sin (3 0^{\circ})

Use the following trivial identity:

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

sin (3 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2}

1 \cdot \frac{1}{2} = 1.495 sin (x)

Switch sides

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

Multiply both sides by

1000

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

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

1.495 sin (x) \cdot 1000 = 1 \cdot \frac{1}{2} \cdot 1000

Refine

1495 sin (x) = 500

1495 sin (x) = 500

Divide both sides by

1495

1495 sin (x) = 500

Divide both sides by

1495

\frac{1495 sin ( x )}{1495} = \frac{500}{1495}

Simplify

sin (x) = \frac{100}{299}

sin (x) = \frac{100}{299}

Apply trig inverse properties

sin (x) = \frac{100}{299}

General solutions for

sin (x) = \frac{100}{299}

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

x = arcsin (\frac{100}{299}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{100}{299}) + 36 0^{\circ} n

x = arcsin (\frac{100}{299}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{100}{299}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.34101 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.34101 \dots + 36 0^{\circ} n

e^{2 c o s (x) - 1} = 1

csc (θ) = - \frac{37}{12}, \frac{3 π}{2} \leq θ \leq 2 π

\frac{3}{2} = 2 \cdot 25 sin (\frac{θ}{2})

sin^{2} (x) - sin (x) - 12 = 0

7 sin (2 ϕ) + 12 cos (ϕ) = 0

What is the general solution for 1sin(30)=1.495sin(x) ?
The general solution for 1sin(30)=1.495sin(x) is x=0.34101…+360n,x=180-0.34101…+360n