What is the general solution for 6sin(pi/4 x)=3 ?

The general solution for 6sin(pi/4 x)=3 is x= 2/3+8n,x= 10/3+8n

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Popular Trigonometry >

6sin(pi/4 x)=3

Solution

6 sin (\frac{π}{4} x) = 3

Solution

x = \frac{2}{3} + 8 n, x = \frac{10}{3} + 8 n

Degrees

x = 38.19718 \dots^{\circ} + 458.36623 \dots^{\circ} n, x = 190.98593 \dots^{\circ} + 458.36623 \dots^{\circ} n

Solution steps

6 sin (\frac{π}{4} x) = 3

Divide both sides by

6

6 sin (\frac{π}{4} x) = 3

Divide both sides by

6

\frac{6 sin ( \frac{π}{4} x )}{6} = \frac{3}{6}

Simplify

sin (\frac{π}{4} x) = \frac{1}{2}

sin (\frac{π}{4} x) = \frac{1}{2}

General solutions for

sin (\frac{π}{4} x) = \frac{1}{2}

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}

\frac{π}{4} x = \frac{π}{6} + 2 πn, \frac{π}{4} x = \frac{5 π}{6} + 2 πn

\frac{π}{4} x = \frac{π}{6} + 2 πn, \frac{π}{4} x = \frac{5 π}{6} + 2 πn

Solve

\frac{π}{4} x = \frac{π}{6} + 2 πn : x = \frac{2}{3} + 8 n

\frac{π}{4} x = \frac{π}{6} + 2 πn

Multiply both sides by

4

\frac{π}{4} x = \frac{π}{6} + 2 πn

Multiply both sides by

4

4 \cdot \frac{π}{4} x = 4 \cdot \frac{π}{6} + 4 \cdot 2 πn

Simplify

4 \cdot \frac{π}{4} x = 4 \cdot \frac{π}{6} + 4 \cdot 2 πn

Simplify

4 \cdot \frac{π}{4} x : π x

4 \cdot \frac{π}{4} x

Multiply fractions:

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

= \frac{4 π}{4} x

Cancel the common factor:

4

= x π

Simplify

4 \cdot \frac{π}{6} + 4 \cdot 2 πn : \frac{2 π}{3} + 8 πn

4 \cdot \frac{π}{6} + 4 \cdot 2 πn

4 \cdot \frac{π}{6} = \frac{2 π}{3}

4 \cdot \frac{π}{6}

Multiply fractions:

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

= \frac{π 4}{6}

Cancel the common factor:

2

= \frac{2 π}{3}

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= 8 πn

= \frac{2 π}{3} + 8 πn

π x = \frac{2 π}{3} + 8 πn

π x = \frac{2 π}{3} + 8 πn

π x = \frac{2 π}{3} + 8 πn

Divide both sides by

π

π x = \frac{2 π}{3} + 8 πn

Divide both sides by

π

\frac{π x}{π} = \frac{\frac{2 π}{3}}{π} + \frac{8 πn}{π}

Simplify

\frac{π x}{π} = \frac{\frac{2 π}{3}}{π} + \frac{8 πn}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{\frac{2 π}{3}}{π} + \frac{8 πn}{π} : \frac{2}{3} + 8 n

\frac{\frac{2 π}{3}}{π} + \frac{8 πn}{π}

\frac{\frac{2 π}{3}}{π} = \frac{2}{3}

\frac{\frac{2 π}{3}}{π}

Apply the fraction rule:

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

= \frac{2 π}{3 π}

Cancel the common factor:

π

= \frac{2}{3}

\frac{8 πn}{π} = 8 n

\frac{8 πn}{π}

Cancel the common factor:

π

= 8 n

= \frac{2}{3} + 8 n

x = \frac{2}{3} + 8 n

x = \frac{2}{3} + 8 n

x = \frac{2}{3} + 8 n

Solve

\frac{π}{4} x = \frac{5 π}{6} + 2 πn : x = \frac{10}{3} + 8 n

\frac{π}{4} x = \frac{5 π}{6} + 2 πn

Multiply both sides by

4

\frac{π}{4} x = \frac{5 π}{6} + 2 πn

Multiply both sides by

4

4 \cdot \frac{π}{4} x = 4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn

Simplify

4 \cdot \frac{π}{4} x = 4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn

Simplify

4 \cdot \frac{π}{4} x : π x

4 \cdot \frac{π}{4} x

Multiply fractions:

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

= \frac{4 π}{4} x

Cancel the common factor:

4

= x π

Simplify

4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn : \frac{10 π}{3} + 8 πn

4 \cdot \frac{5 π}{6} + 4 \cdot 2 πn

4 \cdot \frac{5 π}{6} = \frac{10 π}{3}

4 \cdot \frac{5 π}{6}

Multiply fractions:

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

= \frac{5 π 4}{6}

Multiply the numbers:

5 \cdot 4 = 20

= \frac{20 π}{6}

Cancel the common factor:

2

= \frac{10 π}{3}

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= 8 πn

= \frac{10 π}{3} + 8 πn

π x = \frac{10 π}{3} + 8 πn

π x = \frac{10 π}{3} + 8 πn

π x = \frac{10 π}{3} + 8 πn

Divide both sides by

π

π x = \frac{10 π}{3} + 8 πn

Divide both sides by

π

\frac{π x}{π} = \frac{\frac{10 π}{3}}{π} + \frac{8 πn}{π}

Simplify

\frac{π x}{π} = \frac{\frac{10 π}{3}}{π} + \frac{8 πn}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{\frac{10 π}{3}}{π} + \frac{8 πn}{π} : \frac{10}{3} + 8 n

\frac{\frac{10 π}{3}}{π} + \frac{8 πn}{π}

\frac{\frac{10 π}{3}}{π} = \frac{10}{3}

\frac{\frac{10 π}{3}}{π}

Apply the fraction rule:

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

= \frac{10 π}{3 π}

Cancel the common factor:

π

= \frac{10}{3}

\frac{8 πn}{π} = 8 n

\frac{8 πn}{π}

Cancel the common factor:

π

= 8 n

= \frac{10}{3} + 8 n

x = \frac{10}{3} + 8 n

x = \frac{10}{3} + 8 n

x = \frac{10}{3} + 8 n

x = \frac{2}{3} + 8 n, x = \frac{10}{3} + 8 n

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 6sin(pi/4 x)=3 ?
The general solution for 6sin(pi/4 x)=3 is x= 2/3+8n,x= 10/3+8n