What is the general solution for -900cos(30x)=0 ?

The general solution for -900cos(30x)=0 is x= pi/(60)+(pin)/(15),x= pi/(20)+(pin)/(15)

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Popular Trigonometry >

-900cos(30x)=0

Solution

- 900 cos (30 x) = 0

Solution

x = \frac{π}{60} + \frac{πn}{15}, x = \frac{π}{20} + \frac{πn}{15}

Degrees

x = 3^{\circ} + 1 2^{\circ} n, x = 9^{\circ} + 1 2^{\circ} n

Solution steps

- 900 cos (30 x) = 0

Divide both sides by

- 900

- 900 cos (30 x) = 0

Divide both sides by

- 900

\frac{- 900 cos ( 30 x )}{- 900} = \frac{0}{- 900}

Simplify

cos (30 x) = 0

cos (30 x) = 0

General solutions for

cos (30 x) = 0

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

30 x = \frac{π}{2} + 2 πn, 30 x = \frac{3 π}{2} + 2 πn

30 x = \frac{π}{2} + 2 πn, 30 x = \frac{3 π}{2} + 2 πn

Solve

30 x = \frac{π}{2} + 2 πn : x = \frac{π}{60} + \frac{πn}{15}

30 x = \frac{π}{2} + 2 πn

Divide both sides by

30

30 x = \frac{π}{2} + 2 πn

Divide both sides by

30

\frac{30 x}{30} = \frac{\frac{π}{2}}{30} + \frac{2 πn}{30}

Simplify

\frac{30 x}{30} = \frac{\frac{π}{2}}{30} + \frac{2 πn}{30}

Simplify

\frac{30 x}{30} : x

\frac{30 x}{30}

Divide the numbers:

\frac{30}{30} = 1

= x

Simplify

\frac{\frac{π}{2}}{30} + \frac{2 πn}{30} : \frac{π}{60} + \frac{πn}{15}

\frac{\frac{π}{2}}{30} + \frac{2 πn}{30}

\frac{\frac{π}{2}}{30} = \frac{π}{60}

\frac{\frac{π}{2}}{30}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 30}

Multiply the numbers:

2 \cdot 30 = 60

= \frac{π}{60}

\frac{2 πn}{30} = \frac{πn}{15}

\frac{2 πn}{30}

Cancel the common factor:

2

= \frac{πn}{15}

= \frac{π}{60} + \frac{πn}{15}

x = \frac{π}{60} + \frac{πn}{15}

x = \frac{π}{60} + \frac{πn}{15}

x = \frac{π}{60} + \frac{πn}{15}

Solve

30 x = \frac{3 π}{2} + 2 πn : x = \frac{π}{20} + \frac{πn}{15}

30 x = \frac{3 π}{2} + 2 πn

Divide both sides by

30

30 x = \frac{3 π}{2} + 2 πn

Divide both sides by

30

\frac{30 x}{30} = \frac{\frac{3 π}{2}}{30} + \frac{2 πn}{30}

Simplify

\frac{30 x}{30} = \frac{\frac{3 π}{2}}{30} + \frac{2 πn}{30}

Simplify

\frac{30 x}{30} : x

\frac{30 x}{30}

Divide the numbers:

\frac{30}{30} = 1

= x

Simplify

\frac{\frac{3 π}{2}}{30} + \frac{2 πn}{30} : \frac{π}{20} + \frac{πn}{15}

\frac{\frac{3 π}{2}}{30} + \frac{2 πn}{30}

\frac{\frac{3 π}{2}}{30} = \frac{π}{20}

\frac{\frac{3 π}{2}}{30}

Apply the fraction rule:

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

= \frac{3 π}{2 \cdot 30}

Multiply the numbers:

2 \cdot 30 = 60

= \frac{3 π}{60}

Cancel the common factor:

3

= \frac{π}{20}

\frac{2 πn}{30} = \frac{πn}{15}

\frac{2 πn}{30}

Cancel the common factor:

2

= \frac{πn}{15}

= \frac{π}{20} + \frac{πn}{15}

x = \frac{π}{20} + \frac{πn}{15}

x = \frac{π}{20} + \frac{πn}{15}

x = \frac{π}{20} + \frac{πn}{15}

x = \frac{π}{60} + \frac{πn}{15}, x = \frac{π}{20} + \frac{πn}{15}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for -900cos(30x)=0 ?
The general solution for -900cos(30x)=0 is x= pi/(60)+(pin)/(15),x= pi/(20)+(pin)/(15)