What is the general solution for sin(0.3x)=1 ?

The general solution for sin(0.3x)=1 is x=(5pi)/3+(20pin)/3

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Popular >

sin(0.3x)=1

Solution

sin (0.3 x) = 1

Solution

x = \frac{5 π}{3} + \frac{20 πn}{3}

Degrees

x = 30 0^{\circ} + 120 0^{\circ} n

Solution steps

sin (0.3 x) = 1

General solutions for

sin (0.3 x) = 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

0.3 x = \frac{π}{2} + 2 πn

0.3 x = \frac{π}{2} + 2 πn

Solve

0.3 x = \frac{π}{2} + 2 πn : x = \frac{5 π}{3} + \frac{20 πn}{3}

0.3 x = \frac{π}{2} + 2 πn

Multiply both sides by

10

0.3 x = \frac{π}{2} + 2 πn

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

0.3 x \cdot 10 = \frac{π}{2} \cdot 10 + 2 πn \cdot 10

Refine

3 x = 5 π + 20 πn

3 x = 5 π + 20 πn

Divide both sides by

3

3 x = 5 π + 20 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{5 π}{3} + \frac{20 πn}{3}

Simplify

x = \frac{5 π}{3} + \frac{20 πn}{3}

x = \frac{5 π}{3} + \frac{20 πn}{3}

x = \frac{5 π}{3} + \frac{20 πn}{3}

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cos (x) = \frac{2}{2}

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21.16 = 19.6 sin (x) - 29.4 cos (x)

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Frequently Asked Questions (FAQ)

What is the general solution for sin(0.3x)=1 ?
The general solution for sin(0.3x)=1 is x=(5pi)/3+(20pin)/3