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solvefor x,-cos(x)+1/y =c

Solution

solve for

x, - cos (x) + \frac{1}{y} = c

x = arccos (- \frac{cy - 1}{y}) + 2 πn, x = - arccos (- \frac{cy - 1}{y}) + 2 πn

Solution steps

- cos (x) + \frac{1}{y} = c

Move

\frac{1}{y}

to the right side

- cos (x) + \frac{1}{y} = c

Subtract

\frac{1}{y}

from both sides

- cos (x) + \frac{1}{y} - \frac{1}{y} = c - \frac{1}{y}

Simplify

- cos (x) = c - \frac{1}{y}

- cos (x) = c - \frac{1}{y}

Divide both sides by

- 1

- cos (x) = c - \frac{1}{y}

Divide both sides by

- 1

\frac{- cos ( x )}{- 1} = \frac{c}{- 1} - \frac{\frac{1}{y}}{- 1}

Simplify

\frac{- cos ( x )}{- 1} = \frac{c}{- 1} - \frac{\frac{1}{y}}{- 1}

Simplify

\frac{- cos ( x )}{- 1} : cos (x)

\frac{- cos ( x )}{- 1}

Apply the fraction rule:

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

= \frac{cos ( x )}{1}

Apply rule

\frac{a}{1} = a

= cos (x)

Simplify

\frac{c}{- 1} - \frac{\frac{1}{y}}{- 1} : - \frac{cy - 1}{y}

\frac{c}{- 1} - \frac{\frac{1}{y}}{- 1}

Apply rule

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

= \frac{c - \frac{1}{y}}{- 1}

Apply the fraction rule:

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

= - \frac{c - \frac{1}{y}}{1}

Join

c - \frac{1}{y} : \frac{cy - 1}{y}

c - \frac{1}{y}

Convert element to fraction:

c = \frac{cy}{y}

= \frac{cy}{y} - \frac{1}{y}

Since the denominators are equal, combine the fractions:

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

= \frac{cy - 1}{y}

= - \frac{\frac{cy - 1}{y}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= - \frac{cy - 1}{y}

cos (x) = - \frac{cy - 1}{y}

cos (x) = - \frac{cy - 1}{y}

cos (x) = - \frac{cy - 1}{y}

Apply trig inverse properties

cos (x) = - \frac{cy - 1}{y}

General solutions for

cos (x) = - \frac{cy - 1}{y}

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

x = arccos (- \frac{cy - 1}{y}) + 2 πn, x = - arccos (- \frac{cy - 1}{y}) + 2 πn

x = arccos (- \frac{cy - 1}{y}) + 2 πn, x = - arccos (- \frac{cy - 1}{y}) + 2 πn

cos^{2} (x) - 3 sin (x) - 2 = 0

x, \frac{cos ( x )}{t a g} = \frac{3}{2}

sin^{3} (x) = 2 sin (x)

tan (x) = (\frac{3}{2})

2 sin (3 x) = 1, 0 \leq x \leq 2 π