What is the general solution for sin(-pi/8 c)=-14/14 ?

The general solution for sin(-pi/8 c)=-14/14 is c=-12-16n

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sin(-pi/8 c)=-14/14

Solution

sin (- \frac{π}{8} c) = - \frac{14}{14}

Solution

c = - 12 - 16 n

Degrees

c = - 687.54935 \dots^{\circ} - 916.73247 \dots^{\circ} n

Solution steps

sin (- \frac{π}{8} c) = - \frac{14}{14}

Apply rule

\frac{a}{a} = 1

sin (- \frac{π}{8} c) = - 1

General solutions for

sin (- \frac{π}{8} c) = - 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}{8} c = \frac{3 π}{2} + 2 πn

- \frac{π}{8} c = \frac{3 π}{2} + 2 πn

Solve

- \frac{π}{8} c = \frac{3 π}{2} + 2 πn : c = - 12 - 16 n

- \frac{π}{8} c = \frac{3 π}{2} + 2 πn

Multiply both sides by

8

- \frac{π}{8} c = \frac{3 π}{2} + 2 πn

Multiply both sides by

8

8 (- \frac{π}{8} c) = 8 \cdot \frac{3 π}{2} + 8 \cdot 2 πn

Simplify

8 (- \frac{π}{8} c) = 8 \cdot \frac{3 π}{2} + 8 \cdot 2 πn

Simplify

8 (- \frac{π}{8} c) : - π c

8 (- \frac{π}{8} c)

Remove parentheses:

(- a) = - a

= - 8 \cdot \frac{π}{8} c

Multiply fractions:

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

= - \frac{8 π}{8} c

Cancel the common factor:

8

= - c π

Simplify

8 \cdot \frac{3 π}{2} + 8 \cdot 2 πn : 12 π + 16 πn

8 \cdot \frac{3 π}{2} + 8 \cdot 2 πn

8 \cdot \frac{3 π}{2} = 12 π

8 \cdot \frac{3 π}{2}

Multiply fractions:

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

= \frac{3 π 8}{2}

Multiply the numbers:

3 \cdot 8 = 24

= \frac{24 π}{2}

Divide the numbers:

\frac{24}{2} = 12

= 12 π

8 \cdot 2 πn = 16 πn

8 \cdot 2 πn

Multiply the numbers:

8 \cdot 2 = 16

= 16 πn

= 12 π + 16 πn

- π c = 12 π + 16 πn

- π c = 12 π + 16 πn

- π c = 12 π + 16 πn

Divide both sides by

- π

- π c = 12 π + 16 πn

Divide both sides by

- π

\frac{- π c}{- π} = \frac{12 π}{- π} + \frac{16 πn}{- π}

Simplify

\frac{- π c}{- π} = \frac{12 π}{- π} + \frac{16 πn}{- π}

Simplify

\frac{- π c}{- π} : c

\frac{- π c}{- π}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{π c}{π}

Cancel the common factor:

π

= c

Simplify

\frac{12 π}{- π} + \frac{16 πn}{- π} : - 12 - 16 n

\frac{12 π}{- π} + \frac{16 πn}{- π}

\frac{12 π}{- π} = - 12

\frac{12 π}{- π}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{12 π}{π}

Cancel the common factor:

π

= - 12

= - 12 + \frac{16 πn}{- π}

\frac{16 πn}{- π} = - 16 n

\frac{16 πn}{- π}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{16 πn}{π}

Cancel the common factor:

π

= - 16 n

= - 12 - 16 n

c = - 12 - 16 n

c = - 12 - 16 n

c = - 12 - 16 n

c = - 12 - 16 n

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Frequently Asked Questions (FAQ)

What is the general solution for sin(-pi/8 c)=-14/14 ?
The general solution for sin(-pi/8 c)=-14/14 is c=-12-16n