What is the general solution for -pi/(30)sin(pi/(90)(x+20))=0 ?

The general solution for -pi/(30)sin(pi/(90)(x+20))=0 is x=180n-20,x=180n+70

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Popular Trigonometry >

-pi/(30)sin(pi/(90)(x+20))=0

Solution

- \frac{π}{30} sin (\frac{π}{90} (x + 20)) = 0

Solution

x = 180 n - 20, x = 180 n + 70

Degrees

x = - 1145.91559 \dots^{\circ} + 10313.24031 \dots^{\circ} n, x = 4010.70456 \dots^{\circ} + 10313.24031 \dots^{\circ} n

Solution steps

- \frac{π}{30} sin (\frac{π}{90} (x + 20)) = 0

Multiply both sides by

30

- \frac{π}{30} sin (\frac{π}{90} (x + 20)) = 0

Multiply both sides by

30

30 (- \frac{π}{30} sin (\frac{π}{90} (x + 20))) = 0 \cdot 30

Simplify

- π sin (\frac{π}{90} (x + 20)) = 0

- π sin (\frac{π}{90} (x + 20)) = 0

Divide both sides by

- π

- π sin (\frac{π}{90} (x + 20)) = 0

Divide both sides by

- π

\frac{- π sin ( \frac{π}{90} ( x + 20 ) )}{- π} = \frac{0}{- π}

Simplify

sin (\frac{π}{90} (x + 20)) = 0

sin (\frac{π}{90} (x + 20)) = 0

General solutions for

sin (\frac{π}{90} (x + 20)) = 0

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}{90} (x + 20) = 0 + 2 πn, \frac{π}{90} (x + 20) = π + 2 πn

\frac{π}{90} (x + 20) = 0 + 2 πn, \frac{π}{90} (x + 20) = π + 2 πn

Solve

\frac{π}{90} (x + 20) = 0 + 2 πn : x = 180 n - 20

\frac{π}{90} (x + 20) = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{π}{90} (x + 20) = 2 πn

Multiply both sides by

90

\frac{π}{90} (x + 20) = 2 πn

Multiply both sides by

90

90 \cdot \frac{π}{90} (x + 20) = 90 \cdot 2 πn

Simplify

π (x + 20) = 180 πn

π (x + 20) = 180 πn

Divide both sides by

π

π (x + 20) = 180 πn

Divide both sides by

π

\frac{π ( x + 20 )}{π} = \frac{180 πn}{π}

Simplify

x + 20 = 180 n

x + 20 = 180 n

Move

20

to the right side

x + 20 = 180 n

Subtract

20

from both sides

x + 20 - 20 = 180 n - 20

Simplify

x = 180 n - 20

x = 180 n - 20

Solve

\frac{π}{90} (x + 20) = π + 2 πn : x = 180 n + 70

\frac{π}{90} (x + 20) = π + 2 πn

Multiply both sides by

90

\frac{π}{90} (x + 20) = π + 2 πn

Multiply both sides by

90

90 \cdot \frac{π}{90} (x + 20) = 90 π + 90 \cdot 2 πn

Simplify

π (x + 20) = 90 π + 180 πn

π (x + 20) = 90 π + 180 πn

Divide both sides by

π

π (x + 20) = 90 π + 180 πn

Divide both sides by

π

\frac{π ( x + 20 )}{π} = \frac{90 π}{π} + \frac{180 πn}{π}

Simplify

\frac{π ( x + 20 )}{π} = \frac{90 π}{π} + \frac{180 πn}{π}

Simplify

\frac{π ( x + 20 )}{π} : x + 20

\frac{π ( x + 20 )}{π}

Cancel the common factor:

π

= x + 20

Simplify

\frac{90 π}{π} + \frac{180 πn}{π} : 90 + 180 n

\frac{90 π}{π} + \frac{180 πn}{π}

Cancel

\frac{90 π}{π} : 90

\frac{90 π}{π}

Cancel the common factor:

π

= 90

= 90 + \frac{180 πn}{π}

Cancel

\frac{180 πn}{π} : 180 n

\frac{180 πn}{π}

Cancel the common factor:

π

= 180 n

= 90 + 180 n

x + 20 = 90 + 180 n

x + 20 = 90 + 180 n

x + 20 = 90 + 180 n

Move

20

to the right side

x + 20 = 90 + 180 n

Subtract

20

from both sides

x + 20 - 20 = 90 + 180 n - 20

Simplify

x = 180 n + 70

x = 180 n + 70

x = 180 n - 20, x = 180 n + 70

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for -pi/(30)sin(pi/(90)(x+20))=0 ?
The general solution for -pi/(30)sin(pi/(90)(x+20))=0 is x=180n-20,x=180n+70