What is the general solution for sin(pi/4 x)=1 ?

The general solution for sin(pi/4 x)=1 is x=2+8n

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Popular Trigonometry >

sin(pi/4 x)=1

Solution

sin (\frac{π}{4} x) = 1

Solution

x = 2 + 8 n

Degrees

x = 114.59155 \dots^{\circ} + 458.36623 \dots^{\circ} n

Solution steps

sin (\frac{π}{4} x) = 1

General solutions for

sin (\frac{π}{4} 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}

\frac{π}{4} x = \frac{π}{2} + 2 πn

\frac{π}{4} x = \frac{π}{2} + 2 πn

Solve

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

\frac{π}{4} x = \frac{π}{2} + 2 πn

Multiply both sides by

4

\frac{π}{4} x = \frac{π}{2} + 2 πn

Multiply both sides by

4

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

Simplify

4 \cdot \frac{π}{4} x = 4 \cdot \frac{π}{2} + 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}{2} + 4 \cdot 2 πn : 2 π + 8 πn

4 \cdot \frac{π}{2} + 4 \cdot 2 πn

4 \cdot \frac{π}{2} = 2 π

4 \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{π 4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2 π

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

Multiply the numbers:

4 \cdot 2 = 8

= 8 πn

= 2 π + 8 πn

π x = 2 π + 8 πn

π x = 2 π + 8 πn

π x = 2 π + 8 πn

Divide both sides by

π

π x = 2 π + 8 πn

Divide both sides by

π

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

Simplify

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

Simplify

\frac{π x}{π} : x

\frac{π x}{π}

Cancel the common factor:

π

= x

Simplify

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

\frac{2 π}{π} + \frac{8 πn}{π}

Cancel

\frac{2 π}{π} : 2

\frac{2 π}{π}

Cancel the common factor:

π

= 2

= 2 + \frac{8 πn}{π}

Cancel

\frac{8 πn}{π} : 8 n

\frac{8 πn}{π}

Cancel the common factor:

π

= 8 n

= 2 + 8 n

x = 2 + 8 n

x = 2 + 8 n

x = 2 + 8 n

x = 2 + 8 n

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for sin(pi/4 x)=1 ?
The general solution for sin(pi/4 x)=1 is x=2+8n