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Popular Trigonometry >

(sqrt(17))/8 sin(8sqrt(2)x+1.326)=0

Solution

\frac{17}{8} sin (82 x + 1.326) = 0

Solution

x = 0.55536 \dots n - 0.11720 \dots, x = \frac{π}{11.31370 \dots} - 0.11720 \dots + 0.55536 \dots n

Degrees

x = - 6.71523 \dots^{\circ} + 31.81980 \dots^{\circ} n, x = 9.19466 \dots^{\circ} + 31.81980 \dots^{\circ} n

Solution steps

\frac{17}{8} sin (82 x + 1.326) = 0

Multiply both sides by

8

\frac{17}{8} sin (82 x + 1.326) = 0

Multiply both sides by

8

8 \cdot \frac{17}{8} sin (82 x + 1.326) = 0 \cdot 8

Simplify

17 sin (82 x + 1.326) = 0

17 sin (82 x + 1.326) = 0

Divide both sides by

17

17 sin (82 x + 1.326) = 0

Divide both sides by

17

\frac{17 sin ( 8 2 x + 1.326 )}{17} = \frac{0}{17}

Simplify

sin (82 x + 1.326) = 0

sin (82 x + 1.326) = 0

General solutions for

sin (82 x + 1.326) = 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}

82 x + 1.326 = 0 + 2 πn, 82 x + 1.326 = π + 2 πn

82 x + 1.326 = 0 + 2 πn, 82 x + 1.326 = π + 2 πn

Solve

82 x + 1.326 = 0 + 2 πn : x = 0.55536 \dots n - 0.11720 \dots

82 x + 1.326 = 0 + 2 πn

0 + 2 πn = 2 πn

82 x + 1.326 = 2 πn

Move

1.326

to the right side

82 x + 1.326 = 2 πn

Subtract

1.326

from both sides

82 x + 1.326 - 1.326 = 2 πn - 1.326

Simplify

82 x = 6.28318 \dots n - 1.326

82 x = 6.28318 \dots n - 1.326

Divide both sides by

82

82 x = 6.28318 \dots n - 1.326

Divide both sides by

82

\frac{8 2 x}{8 2} = \frac{6.28318 \dots n}{8 2} - \frac{1.326}{8 2}

Simplify

\frac{8 2 x}{8 2} = \frac{6.28318 \dots n}{8 2} - \frac{1.326}{8 2}

Simplify

\frac{8 2 x}{8 2} : x

\frac{8 2 x}{8 2}

Divide the numbers:

\frac{8}{8} = 1

= \frac{2 x}{2}

Cancel the common factor:

2

= x

Simplify

\frac{6.28318 \dots n}{8 2} - \frac{1.326}{8 2} : 0.55536 \dots n - 0.11720 \dots

\frac{6.28318 \dots n}{8 2} - \frac{1.326}{8 2}

\frac{6.28318 \dots n}{8 2} = 0.55536 \dots n

\frac{6.28318 \dots n}{8 2}

Convert element to a decimal form

2 = 1.41421 \dots

= \frac{6.28318 \dots n}{8 \cdot 1.41421 \dots}

Multiply the numbers:

8 \cdot 1.41421 \dots = 11.31370 \dots

= \frac{6.28318 \dots n}{11.31370 \dots}

Divide the numbers:

\frac{6.28318 \dots}{11.31370 \dots} = 0.55536 \dots

= 0.55536 \dots n

\frac{1.326}{8 2} = 0.11720 \dots

\frac{1.326}{8 2}

Convert element to a decimal form

2 = 1.41421 \dots

= \frac{1.326}{8 \cdot 1.41421 \dots}

Multiply the numbers:

8 \cdot 1.41421 \dots = 11.31370 \dots

= \frac{1.326}{11.31370 \dots}

Divide the numbers:

\frac{1.326}{11.31370 \dots} = 0.11720 \dots

= 0.11720 \dots

= 0.55536 \dots n - 0.11720 \dots

x = 0.55536 \dots n - 0.11720 \dots

x = 0.55536 \dots n - 0.11720 \dots

x = 0.55536 \dots n - 0.11720 \dots

Solve

82 x + 1.326 = π + 2 πn : x = \frac{π}{11.31370 \dots} - 0.11720 \dots + 0.55536 \dots n

82 x + 1.326 = π + 2 πn

Move

1.326

to the right side

82 x + 1.326 = π + 2 πn

Subtract

1.326

from both sides

82 x + 1.326 - 1.326 = π + 2 πn - 1.326

Simplify

82 x = π + 6.28318 \dots n - 1.326

82 x = π + 6.28318 \dots n - 1.326

Divide both sides by

82

82 x = π + 6.28318 \dots n - 1.326

Divide both sides by

82

\frac{8 2 x}{8 2} = \frac{π}{8 2} + \frac{6.28318 \dots n}{8 2} - \frac{1.326}{8 2}

Simplify

\frac{8 2 x}{8 2} = \frac{π}{8 2} + \frac{6.28318 \dots n}{8 2} - \frac{1.326}{8 2}

Simplify

\frac{8 2 x}{8 2} : x

\frac{8 2 x}{8 2}

Divide the numbers:

\frac{8}{8} = 1

= \frac{2 x}{2}

Cancel the common factor:

2

= x

Simplify

\frac{π}{8 2} + \frac{6.28318 \dots n}{8 2} - \frac{1.326}{8 2} : \frac{π}{11.31370 \dots} - 0.11720 \dots + 0.55536 \dots n

\frac{π}{8 2} + \frac{6.28318 \dots n}{8 2} - \frac{1.326}{8 2}

Group like terms

= \frac{π}{8 2} - \frac{1.326}{8 2} + \frac{6.28318 \dots n}{8 2}

\frac{π}{8 2} = \frac{π}{11.31370 \dots}

\frac{π}{8 2}

Convert element to a decimal form

2 = 1.41421 \dots

= \frac{π}{8 \cdot 1.41421 \dots}

Multiply the numbers:

8 \cdot 1.41421 \dots = 11.31370 \dots

= \frac{π}{11.31370 \dots}

\frac{1.326}{8 2} = 0.11720 \dots

\frac{1.326}{8 2}

Convert element to a decimal form

2 = 1.41421 \dots

= \frac{1.326}{8 \cdot 1.41421 \dots}

Multiply the numbers:

8 \cdot 1.41421 \dots = 11.31370 \dots

= \frac{1.326}{11.31370 \dots}

Divide the numbers:

\frac{1.326}{11.31370 \dots} = 0.11720 \dots

= 0.11720 \dots

\frac{6.28318 \dots n}{8 2} = 0.55536 \dots n

\frac{6.28318 \dots n}{8 2}

Convert element to a decimal form

2 = 1.41421 \dots

= \frac{6.28318 \dots n}{8 \cdot 1.41421 \dots}

Multiply the numbers:

8 \cdot 1.41421 \dots = 11.31370 \dots

= \frac{6.28318 \dots n}{11.31370 \dots}

Divide the numbers:

\frac{6.28318 \dots}{11.31370 \dots} = 0.55536 \dots

= 0.55536 \dots n

= \frac{π}{11.31370 \dots} - 0.11720 \dots + 0.55536 \dots n

x = \frac{π}{11.31370 \dots} - 0.11720 \dots + 0.55536 \dots n

x = \frac{π}{11.31370 \dots} - 0.11720 \dots + 0.55536 \dots n

x = \frac{π}{11.31370 \dots} - 0.11720 \dots + 0.55536 \dots n

x = 0.55536 \dots n - 0.11720 \dots, x = \frac{π}{11.31370 \dots} - 0.11720 \dots + 0.55536 \dots n

Graph

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