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Popular Trigonometry >

(5009.8l(1-cos(θ)))=0.018

Solution

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

Solution

θ = arccos (- \frac{3.67347 E - 6 - l}{l}) + 2 πn, θ = - arccos (- \frac{3.67347 E - 6 - l}{l}) + 2 πn

Solution steps

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

Divide both sides by

4900 l; l \neq = 0

500 \cdot 9.8 l (1 - cos (θ)) = 0.018

Divide both sides by

4900 l; l \neq = 0

\frac{500 \cdot 9.8 l ( 1 - cos ( θ ) )}{4900 l} = \frac{0.018}{4900 l}; l \neq = 0

Simplify

1 - cos (θ) = \frac{3.67347 E - 6}{l}; l \neq = 0

1 - cos (θ) = \frac{3.67347 E - 6}{l}; l \neq = 0

Move

1

to the right side

1 - cos (θ) = \frac{3.67347 E - 6}{l}; l \neq = 0

Subtract

1

from both sides

1 - cos (θ) - 1 = \frac{3.67347 E - 6}{l} - 1; l \neq = 0

Simplify

- cos (θ) = \frac{3.67347 E - 6}{l} - 1; l \neq = 0

- cos (θ) = \frac{3.67347 E - 6}{l} - 1; l \neq = 0

Divide both sides by

- 1; l \neq = 0

- cos (θ) = \frac{3.67347 E - 6}{l} - 1; l \neq = 0

Divide both sides by

- 1; l \neq = 0

\frac{- cos ( θ )}{- 1} = \frac{\frac{3.67347 E - 6}{l}}{- 1} - \frac{1}{- 1}; l \neq = 0

Simplify

\frac{- cos ( θ )}{- 1} = \frac{\frac{3.67347 E - 6}{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{3.67347 E - 6}{l}}{- 1} - \frac{1}{- 1} : - \frac{3.67347 E - 6 - l}{l}

\frac{\frac{3.67347 E - 6}{l}}{- 1} - \frac{1}{- 1}

Apply rule

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

= \frac{\frac{3.67347 E - 6}{l} - 1}{- 1}

Apply the fraction rule:

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

= - \frac{\frac{3.67347 E - 6}{l} - 1}{1}

Join

\frac{3.67347 E - 6}{l} - 1 : \frac{3.67347 E - 6 - l}{l}

\frac{3.67347 E - 6}{l} - 1

Convert element to fraction:

1 = \frac{1 l}{l}

= \frac{3.67347 E - 6}{l} - \frac{1 \cdot l}{l}

Since the denominators are equal, combine the fractions:

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

= \frac{3.67347 E - 6 - 1 \cdot l}{l}

Multiply:

1 \cdot l = l

= \frac{3.67347 E - 6 - l}{l}

= - \frac{\frac{- l + 3.67347 E - 6}{l}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= - \frac{- l + 3.67347 E - 6}{l}

cos (θ) = - \frac{3.67347 E - 6 - l}{l}; l \neq = 0

cos (θ) = - \frac{3.67347 E - 6 - l}{l}; l \neq = 0

cos (θ) = - \frac{3.67347 E - 6 - l}{l}; l \neq = 0

Apply trig inverse properties

cos (θ) = - \frac{3.67347 E - 6 - l}{l}

General solutions for

cos (θ) = - \frac{3.67347 E - 6 - l}{l}

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

θ = arccos (- \frac{3.67347 E - 6 - l}{l}) + 2 πn, θ = - arccos (- \frac{3.67347 E - 6 - l}{l}) + 2 πn

θ = arccos (- \frac{3.67347 E - 6 - l}{l}) + 2 πn, θ = - arccos (- \frac{3.67347 E - 6 - l}{l}) + 2 πn

Graph

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(500*9.8*l(1-cos(θ)))=0.018

Solution

Solution

Graph

Popular Examples

(5009.8l(1-cos(θ)))=0.018