What is the general solution for solvefor x,y=3cos(fxx+pi/2)+5 ?

The general solution for solvefor x,y=3cos(fxx+pi/2)+5 is

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Popular Trigonometry >

solvefor x,y=3cos(fxx+pi/2)+5

Solution

solvefor

Solution

x = \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}

Solution steps

y = 3 cos (f xx + \frac{π}{2}) + 5

Switch sides

3 cos (f xx + \frac{π}{2}) + 5 = y

Move

5

to the right side

3 cos (f xx + \frac{π}{2}) + 5 = y

Subtract

5

from both sides

3 cos (f xx + \frac{π}{2}) + 5 - 5 = y - 5

Simplify

3 cos (f xx + \frac{π}{2}) = y - 5

3 cos (f xx + \frac{π}{2}) = y - 5

Divide both sides by

3

3 cos (f xx + \frac{π}{2}) = y - 5

Divide both sides by

3

\frac{3 cos ( f xx + \frac{π}{2} )}{3} = \frac{y}{3} - \frac{5}{3}

Simplify

\frac{3 cos ( f xx + \frac{π}{2} )}{3} = \frac{y}{3} - \frac{5}{3}

Simplify

\frac{3 cos ( f xx + \frac{π}{2} )}{3} : cos (f xx + \frac{π}{2})

\frac{3 cos ( f xx + \frac{π}{2} )}{3}

Divide the numbers:

\frac{3}{3} = 1

= cos (f xx + \frac{π}{2})

Simplify

\frac{y}{3} - \frac{5}{3} : \frac{y - 5}{3}

\frac{y}{3} - \frac{5}{3}

Apply rule

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

= \frac{y - 5}{3}

cos (f xx + \frac{π}{2}) = \frac{y - 5}{3}

cos (f xx + \frac{π}{2}) = \frac{y - 5}{3}

cos (f xx + \frac{π}{2}) = \frac{y - 5}{3}

Apply trig inverse properties

cos (f xx + \frac{π}{2}) = \frac{y - 5}{3}

General solutions for

cos (f xx + \frac{π}{2}) = \frac{y - 5}{3}

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

f xx + \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn, f xx + \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn

f xx + \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn, f xx + \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn

Solve

f xx + \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn : x = \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

f xx + \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn

Move

\frac{π}{2}

to the right side

f xx + \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn

Subtract

\frac{π}{2}

from both sides

f xx + \frac{π}{2} - \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Simplify

f xx = arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

f xx = arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Simplify

x^{2} f = arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Divide both sides by

f; f \neq = 0

\frac{x ^{2} f}{f} = \frac{arccos ( \frac{y - 5}{3} ) + 2 πn - \frac{π}{2}}{f}; f \neq = 0

x^{2} = \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

Solve

f xx + \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn : x = \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

f xx + \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn

Move

\frac{π}{2}

to the right side

f xx + \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn

Subtract

\frac{π}{2}

from both sides

f xx + \frac{π}{2} - \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Simplify

f xx = - arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

f xx = - arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Simplify

x^{2} f = - arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Divide both sides by

f; f \neq = 0

\frac{x ^{2} f}{f} = \frac{- arccos ( \frac{y - 5}{3} ) + 2 πn - \frac{π}{2}}{f}; f \neq = 0

x^{2} = \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

x = \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor x,y=3cos(fxx+pi/2)+5 ?
The general solution for solvefor x,y=3cos(fxx+pi/2)+5 is