What is the general solution for 1sin(30)=1.5sin(x) ?

The general solution for 1sin(30)=1.5sin(x) is x=0.33983…+360n,x=180-0.33983…+360n

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1sin(30)=1.5sin(x)

Solution

1 sin (3 0^{\circ}) = 1.5 sin (x)

Solution

x = 0.33983 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.33983 \dots + 36 0^{\circ} n

Radians

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

Solution steps

1 \cdot sin (3 0^{\circ}) = 1.5 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} = 1.5 sin (x)

Switch sides

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

Multiply both sides by

10

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

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

1.5 sin (x) \cdot 10 = 1 \cdot \frac{1}{2} \cdot 10

Refine

15 sin (x) = 5

15 sin (x) = 5

Divide both sides by

15

15 sin (x) = 5

Divide both sides by

15

\frac{15 sin ( x )}{15} = \frac{5}{15}

Simplify

sin (x) = \frac{1}{3}

sin (x) = \frac{1}{3}

Apply trig inverse properties

sin (x) = \frac{1}{3}

General solutions for

sin (x) = \frac{1}{3}

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

x = arcsin (\frac{1}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{1}{3}) + 36 0^{\circ} n

x = arcsin (\frac{1}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{1}{3}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.33983 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.33983 \dots + 36 0^{\circ} n

Popular Examples

3-3sin(t)=3sqrt(3)cos(t)

3 - 3 sin (t) = 33 cos (t)

sin(θ)= 3/10

sin (θ) = \frac{3}{10}

30arctan(x)=5pi

30 arctan (x) = 5 π

cosh(2x)-10cosh(x)+13=0

cosh (2 x) - 10 cosh (x) + 13 = 0

sqrt(3)sin(x)-sin(2x)=0

3 sin (x) - sin (2 x) = 0

Frequently Asked Questions (FAQ)

What is the general solution for 1sin(30)=1.5sin(x) ?
The general solution for 1sin(30)=1.5sin(x) is x=0.33983…+360n,x=180-0.33983…+360n