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Popular Trigonometry >

(0.59.8l(1-cos(θ)))=0.018

Solution

(0.5 \cdot 9.8 \cdot l (1 - cos (θ))) = 0.018

Solution

θ = arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn, θ = - arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn

Solution steps

(0.5 \cdot 9.8 l (1 - cos (θ))) = 0.018

Multiply both sides by

1000

0.5 \cdot 9.8 l (1 - cos (θ)) = 0.018

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

0.5 \cdot 9.8 l (1 - cos (θ)) \cdot 1000 = 0.018 \cdot 1000

Refine

4900 l (1 - cos (θ)) = 18

4900 l (1 - cos (θ)) = 18

Divide both sides by

4900 l; l \neq = 0

4900 l (1 - cos (θ)) = 18

Divide both sides by

4900 l; l \neq = 0

\frac{4900 l ( 1 - cos ( θ ) )}{4900 l} = \frac{18}{4900 l}; l \neq = 0

Simplify

1 - cos (θ) = \frac{9}{2450 l}; l \neq = 0

1 - cos (θ) = \frac{9}{2450 l}; l \neq = 0

Move

1

to the right side

1 - cos (θ) = \frac{9}{2450 l}; l \neq = 0

Subtract

1

from both sides

1 - cos (θ) - 1 = \frac{9}{2450 l} - 1; l \neq = 0

Simplify

- cos (θ) = \frac{9}{2450 l} - 1; l \neq = 0

- cos (θ) = \frac{9}{2450 l} - 1; l \neq = 0

Divide both sides by

- 1; l \neq = 0

- cos (θ) = \frac{9}{2450 l} - 1; l \neq = 0

Divide both sides by

- 1; l \neq = 0

\frac{- cos ( θ )}{- 1} = \frac{\frac{9}{2450 l}}{- 1} - \frac{1}{- 1}; l \neq = 0

Simplify

\frac{- cos ( θ )}{- 1} = \frac{\frac{9}{2450 l}}{- 1} - \frac{1}{- 1}

Simplify

\frac{- cos ( θ )}{- 1} : cos (θ)

\frac{- cos ( θ )}{- 1}

Apply the fraction rule:

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

= \frac{cos ( θ )}{1}

Apply rule

\frac{a}{1} = a

= cos (θ)

Simplify

\frac{\frac{9}{2450 l}}{- 1} - \frac{1}{- 1} : - \frac{9 - 2450 l}{2450 l}

\frac{\frac{9}{2450 l}}{- 1} - \frac{1}{- 1}

Apply rule

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

= \frac{\frac{9}{2450 l} - 1}{- 1}

Apply the fraction rule:

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

= - \frac{\frac{9}{2450 l} - 1}{1}

Join

\frac{9}{2450 l} - 1 : \frac{9 - 2450 l}{2450 l}

\frac{9}{2450 l} - 1

Convert element to fraction:

1 = \frac{1 \cdot 2450 l}{2450 l}

= \frac{9}{2450 l} - \frac{1 \cdot 2450 l}{2450 l}

Since the denominators are equal, combine the fractions:

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

= \frac{9 - 1 \cdot 2450 l}{2450 l}

Multiply the numbers:

1 \cdot 2450 = 2450

= \frac{9 - 2450 l}{2450 l}

= - \frac{\frac{- 2450 l + 9}{2450 l}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= - \frac{- 2450 l + 9}{2450 l}

cos (θ) = - \frac{9 - 2450 l}{2450 l}; l \neq = 0

cos (θ) = - \frac{9 - 2450 l}{2450 l}; l \neq = 0

cos (θ) = - \frac{9 - 2450 l}{2450 l}; l \neq = 0

Apply trig inverse properties

cos (θ) = - \frac{9 - 2450 l}{2450 l}

General solutions for

cos (θ) = - \frac{9 - 2450 l}{2450 l}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

θ = arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn, θ = - arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn

θ = arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn, θ = - arccos (- \frac{9 - 2450 l}{2450 l}) + 2 πn

Graph

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(0.5*9.8*l(1-cos(θ)))=0.018

Solution

Solution

Graph

Popular Examples

(0.59.8l(1-cos(θ)))=0.018