What is the general solution for 3sin(pi/5 x)=2 ?

The general solution for 3sin(pi/5 x)=2 is x=(5*0.72972…)/pi+10n,x=5-(5*0.72972…)/pi+10n

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Popular Trigonometry >

3sin(pi/5 x)=2

Solution

3 sin (\frac{π}{5} x) = 2

Solution

x = \frac{5 \cdot 0.72972 \dots}{π} + 10 n, x = 5 - \frac{5 \cdot 0.72972 \dots}{π} + 10 n

Degrees

x = 66.54318 \dots^{\circ} + 572.95779 \dots^{\circ} n, x = 219.93571 \dots^{\circ} + 572.95779 \dots^{\circ} n

Solution steps

3 sin (\frac{π}{5} x) = 2

Divide both sides by

3

3 sin (\frac{π}{5} x) = 2

Divide both sides by

3

\frac{3 sin ( \frac{π}{5} x )}{3} = \frac{2}{3}

Simplify

sin (\frac{π}{5} x) = \frac{2}{3}

sin (\frac{π}{5} x) = \frac{2}{3}

Apply trig inverse properties

sin (\frac{π}{5} x) = \frac{2}{3}

General solutions for

sin (\frac{π}{5} x) = \frac{2}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn, \frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn, \frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn

Solve

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn : x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn

Multiply both sides by

5

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn

Multiply both sides by

5

5 \cdot \frac{π}{5} x = 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

Simplify

5 \cdot \frac{π}{5} x = 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

Simplify

5 \cdot \frac{π}{5} x : π x

5 \cdot \frac{π}{5} x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 π}{5} x

Cancel the common factor:

5

= x π

Simplify

5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn : 5 arcsin (\frac{2}{3}) + 10 πn

5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

Multiply the numbers:

5 \cdot 2 = 10

= 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 arcsin (\frac{2}{3}) + 10 πn

Divide both sides by

π

π x = 5 arcsin (\frac{2}{3}) + 10 πn

Divide both sides by

π

\frac{π x}{π} = \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

Simplify

x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

Solve

\frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn : x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

\frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn

Multiply both sides by

5

\frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn

Multiply both sides by

5

5 \cdot \frac{π}{5} x = 5 π - 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

Simplify

5 \cdot \frac{π}{5} x = 5 π - 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

Simplify

5 \cdot \frac{π}{5} x : π x

5 \cdot \frac{π}{5} x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 π}{5} x

Cancel the common factor:

5

= x π

Simplify

5 π - 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn : 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

5 π - 5 arcsin (\frac{2}{3}) + 5 \cdot 2 πn

Multiply the numbers:

5 \cdot 2 = 10

= 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

Divide both sides by

π

π x = 5 π - 5 arcsin (\frac{2}{3}) + 10 πn

Divide both sides by

π

\frac{π x}{π} = \frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

Simplify

\frac{π x}{π} = \frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π} : 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

\frac{5 π}{π} - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

Cancel

\frac{5 π}{π} : 5

\frac{5 π}{π}

Cancel the common factor:

π

= 5

= 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + \frac{10 πn}{π}

Cancel

\frac{10 πn}{π} : 10 n

\frac{10 πn}{π}

Cancel the common factor:

π

= 10 n

= 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n, x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

Show solutions in decimal form

x = \frac{5 \cdot 0.72972 \dots}{π} + 10 n, x = 5 - \frac{5 \cdot 0.72972 \dots}{π} + 10 n

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 3sin(pi/5 x)=2 ?
The general solution for 3sin(pi/5 x)=2 is x=(5*0.72972…)/pi+10n,x=5-(5*0.72972…)/pi+10n