What is the general solution for solvefor w,100cos(10w)=50 ?

The general solution for solvefor w,100cos(10w)=50 is w= pi/(30)+(pin)/5 ,w= pi/6+(pin)/5

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solvefor w,100cos(10w)=50

Solution

solve for

w, 100 cos (10 w) = 50

Solution

w = \frac{π}{30} + \frac{πn}{5}, w = \frac{π}{6} + \frac{πn}{5}

Degrees

w = 6^{\circ} + 3 6^{\circ} n, w = 3 0^{\circ} + 3 6^{\circ} n

Solution steps

100 cos (10 w) = 50

Divide both sides by

100

100 cos (10 w) = 50

Divide both sides by

100

\frac{100 cos ( 10 w )}{100} = \frac{50}{100}

Simplify

cos (10 w) = \frac{1}{2}

cos (10 w) = \frac{1}{2}

General solutions for

cos (10 w) = \frac{1}{2}

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}

10 w = \frac{π}{3} + 2 πn, 10 w = \frac{5 π}{3} + 2 πn

10 w = \frac{π}{3} + 2 πn, 10 w = \frac{5 π}{3} + 2 πn

Solve

10 w = \frac{π}{3} + 2 πn : w = \frac{π}{30} + \frac{πn}{5}

10 w = \frac{π}{3} + 2 πn

Divide both sides by

10

10 w = \frac{π}{3} + 2 πn

Divide both sides by

10

\frac{10 w}{10} = \frac{\frac{π}{3}}{10} + \frac{2 πn}{10}

Simplify

\frac{10 w}{10} = \frac{\frac{π}{3}}{10} + \frac{2 πn}{10}

Simplify

\frac{10 w}{10} : w

\frac{10 w}{10}

Divide the numbers:

\frac{10}{10} = 1

= w

Simplify

\frac{\frac{π}{3}}{10} + \frac{2 πn}{10} : \frac{π}{30} + \frac{πn}{5}

\frac{\frac{π}{3}}{10} + \frac{2 πn}{10}

\frac{\frac{π}{3}}{10} = \frac{π}{30}

\frac{\frac{π}{3}}{10}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 10}

Multiply the numbers:

3 \cdot 10 = 30

= \frac{π}{30}

\frac{2 πn}{10} = \frac{πn}{5}

\frac{2 πn}{10}

Cancel the common factor:

2

= \frac{πn}{5}

= \frac{π}{30} + \frac{πn}{5}

w = \frac{π}{30} + \frac{πn}{5}

w = \frac{π}{30} + \frac{πn}{5}

w = \frac{π}{30} + \frac{πn}{5}

Solve

10 w = \frac{5 π}{3} + 2 πn : w = \frac{π}{6} + \frac{πn}{5}

10 w = \frac{5 π}{3} + 2 πn

Divide both sides by

10

10 w = \frac{5 π}{3} + 2 πn

Divide both sides by

10

\frac{10 w}{10} = \frac{\frac{5 π}{3}}{10} + \frac{2 πn}{10}

Simplify

\frac{10 w}{10} = \frac{\frac{5 π}{3}}{10} + \frac{2 πn}{10}

Simplify

\frac{10 w}{10} : w

\frac{10 w}{10}

Divide the numbers:

\frac{10}{10} = 1

= w

Simplify

\frac{\frac{5 π}{3}}{10} + \frac{2 πn}{10} : \frac{π}{6} + \frac{πn}{5}

\frac{\frac{5 π}{3}}{10} + \frac{2 πn}{10}

\frac{\frac{5 π}{3}}{10} = \frac{π}{6}

\frac{\frac{5 π}{3}}{10}

Apply the fraction rule:

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

= \frac{5 π}{3 \cdot 10}

Multiply the numbers:

3 \cdot 10 = 30

= \frac{5 π}{30}

Cancel the common factor:

5

= \frac{π}{6}

\frac{2 πn}{10} = \frac{πn}{5}

\frac{2 πn}{10}

Cancel the common factor:

2

= \frac{πn}{5}

= \frac{π}{6} + \frac{πn}{5}

w = \frac{π}{6} + \frac{πn}{5}

w = \frac{π}{6} + \frac{πn}{5}

w = \frac{π}{6} + \frac{πn}{5}

w = \frac{π}{30} + \frac{πn}{5}, w = \frac{π}{6} + \frac{πn}{5}

Popular Examples

cos(θ)= 8/25

cos (θ) = \frac{8}{25}

sin(2x)=pi

sin (2 x) = π

sin(x+5pi)=0

sin (x + 5 π) = 0

cos(2x)+9cos(x)+5=0

cos (2 x) + 9 cos (x) + 5 = 0

25=-20cos((2pi)/(365)(x+10))+25

25 = - 20 cos (\frac{2 π}{365} (x + 10)) + 25

Frequently Asked Questions (FAQ)

What is the general solution for solvefor w,100cos(10w)=50 ?
The general solution for solvefor w,100cos(10w)=50 is w= pi/(30)+(pin)/5 ,w= pi/6+(pin)/5