What is the general solution for 5sin(pi/4 x)=4 ?

The general solution for 5sin(pi/4 x)=4 is x=(4*0.92729…)/pi+8n,x=4-(4*0.92729…)/pi+8n

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5sin(pi/4 x)=4

Solution

5 sin (\frac{π}{4} x) = 4

Solution

x = \frac{4 \cdot 0.92729 \dots}{π} + 8 n, x = 4 - \frac{4 \cdot 0.92729 \dots}{π} + 8 n

Degrees

x = 67.64734 \dots^{\circ} + 458.36623 \dots^{\circ} n, x = 161.53577 \dots^{\circ} + 458.36623 \dots^{\circ} n

Solution steps

5 sin (\frac{π}{4} x) = 4

Divide both sides by

5

5 sin (\frac{π}{4} x) = 4

Divide both sides by

5

\frac{5 sin ( \frac{π}{4} x )}{5} = \frac{4}{5}

Simplify

sin (\frac{π}{4} x) = \frac{4}{5}

sin (\frac{π}{4} x) = \frac{4}{5}

Apply trig inverse properties

sin (\frac{π}{4} x) = \frac{4}{5}

General solutions for

sin (\frac{π}{4} x) = \frac{4}{5}

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

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn, \frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn, \frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn

Solve

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn : x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn

Multiply both sides by

4

\frac{π}{4} x = arcsin (\frac{4}{5}) + 2 πn

Multiply both sides by

4

4 \cdot \frac{π}{4} x = 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

Simplify

4 \cdot \frac{π}{4} x = 4 arcsin (\frac{4}{5}) + 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 arcsin (\frac{4}{5}) + 4 \cdot 2 πn : 4 arcsin (\frac{4}{5}) + 8 πn

4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 arcsin (\frac{4}{5}) + 8 πn

Divide both sides by

π

π x = 4 arcsin (\frac{4}{5}) + 8 πn

Divide both sides by

π

\frac{π x}{π} = \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

Simplify

x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

Solve

\frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn : x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

\frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn

Multiply both sides by

4

\frac{π}{4} x = π - arcsin (\frac{4}{5}) + 2 πn

Multiply both sides by

4

4 \cdot \frac{π}{4} x = 4 π - 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

Simplify

4 \cdot \frac{π}{4} x = 4 π - 4 arcsin (\frac{4}{5}) + 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 π - 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn : 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

4 π - 4 arcsin (\frac{4}{5}) + 4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

Divide both sides by

π

π x = 4 π - 4 arcsin (\frac{4}{5}) + 8 πn

Divide both sides by

π

\frac{π x}{π} = \frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

Simplify

\frac{π x}{π} = \frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

\frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π} : 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

\frac{4 π}{π} - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

Cancel

\frac{4 π}{π} : 4

\frac{4 π}{π}

Cancel the common factor:

π

= 4

= 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + \frac{8 πn}{π}

Cancel

\frac{8 πn}{π} : 8 n

\frac{8 πn}{π}

Cancel the common factor:

π

= 8 n

= 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

x = \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n, x = 4 - \frac{4 arcsin ( \frac{4}{5} )}{π} + 8 n

Show solutions in decimal form

x = \frac{4 \cdot 0.92729 \dots}{π} + 8 n, x = 4 - \frac{4 \cdot 0.92729 \dots}{π} + 8 n

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Frequently Asked Questions (FAQ)

What is the general solution for 5sin(pi/4 x)=4 ?
The general solution for 5sin(pi/4 x)=4 is x=(4*0.92729…)/pi+8n,x=4-(4*0.92729…)/pi+8n