What is the general solution for 120=120sin(pi/3 c) ?

The general solution for 120=120sin(pi/3 c) is c= 3/2+6n

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120=120sin(pi/3 c)

Solution

120 = 120 sin (\frac{π}{3} c)

Solution

c = \frac{3}{2} + 6 n

Degrees

c = 85.94366 \dots^{\circ} + 343.77467 \dots^{\circ} n

Solution steps

120 = 120 sin (\frac{π}{3} c)

Switch sides

120 sin (\frac{π}{3} c) = 120

Divide both sides by

120

120 sin (\frac{π}{3} c) = 120

Divide both sides by

120

\frac{120 sin ( \frac{π}{3} c )}{120} = \frac{120}{120}

Simplify

sin (\frac{π}{3} c) = 1

sin (\frac{π}{3} c) = 1

General solutions for

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

\frac{π}{3} c = \frac{π}{2} + 2 πn

Solve

\frac{π}{3} c = \frac{π}{2} + 2 πn : c = \frac{3}{2} + 6 n

\frac{π}{3} c = \frac{π}{2} + 2 πn

Multiply both sides by

3

\frac{π}{3} c = \frac{π}{2} + 2 πn

Multiply both sides by

3

3 \cdot \frac{π}{3} c = 3 \cdot \frac{π}{2} + 3 \cdot 2 πn

Simplify

3 \cdot \frac{π}{3} c = 3 \cdot \frac{π}{2} + 3 \cdot 2 πn

Simplify

3 \cdot \frac{π}{3} c : π c

3 \cdot \frac{π}{3} c

Multiply fractions:

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

= \frac{3 π}{3} c

Cancel the common factor:

3

= c π

Simplify

3 \cdot \frac{π}{2} + 3 \cdot 2 πn : \frac{3 π}{2} + 6 πn

3 \cdot \frac{π}{2} + 3 \cdot 2 πn

Multiply

3 \cdot \frac{π}{2} : \frac{3 π}{2}

3 \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{π 3}{2}

= \frac{3 π}{2} + 3 \cdot 2 πn

Multiply the numbers:

3 \cdot 2 = 6

= \frac{3 π}{2} + 6 πn

π c = \frac{3 π}{2} + 6 πn

π c = \frac{3 π}{2} + 6 πn

π c = \frac{3 π}{2} + 6 πn

Divide both sides by

π

π c = \frac{3 π}{2} + 6 πn

Divide both sides by

π

\frac{π c}{π} = \frac{\frac{3 π}{2}}{π} + \frac{6 πn}{π}

Simplify

\frac{π c}{π} = \frac{\frac{3 π}{2}}{π} + \frac{6 πn}{π}

Simplify

\frac{π c}{π} : c

\frac{π c}{π}

Cancel the common factor:

π

= c

Simplify

\frac{\frac{3 π}{2}}{π} + \frac{6 πn}{π} : \frac{3}{2} + 6 n

\frac{\frac{3 π}{2}}{π} + \frac{6 πn}{π}

\frac{\frac{3 π}{2}}{π} = \frac{3}{2}

\frac{\frac{3 π}{2}}{π}

Apply the fraction rule:

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

= \frac{3 π}{2 π}

Cancel the common factor:

π

= \frac{3}{2}

\frac{6 πn}{π} = 6 n

\frac{6 πn}{π}

Cancel the common factor:

π

= 6 n

= \frac{3}{2} + 6 n

c = \frac{3}{2} + 6 n

c = \frac{3}{2} + 6 n

c = \frac{3}{2} + 6 n

c = \frac{3}{2} + 6 n

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Frequently Asked Questions (FAQ)

What is the general solution for 120=120sin(pi/3 c) ?
The general solution for 120=120sin(pi/3 c) is c= 3/2+6n