What is the general solution for cos(pi/2-x)= 4/5 ?

The general solution for cos(pi/2-x)= 4/5 is x=-2pin+pi/2-0.64350…,x=-2pi-2pin+pi/2+0.64350…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometry >

cos(pi/2-x)= 4/5

Solution

cos (\frac{π}{2} - x) = \frac{4}{5}

Solution

x = - 2 πn + \frac{π}{2} - 0.64350 \dots, x = - 2 π - 2 πn + \frac{π}{2} + 0.64350 \dots

Degrees

x = 53.13010 \dots^{\circ} - 36 0^{\circ} n, x = - 233.13010 \dots^{\circ} - 36 0^{\circ} n

Solution steps

cos (\frac{π}{2} - x) = \frac{4}{5}

Apply trig inverse properties

cos (\frac{π}{2} - x) = \frac{4}{5}

General solutions for

cos (\frac{π}{2} - x) = \frac{4}{5}

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

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

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

Solve

\frac{π}{2} - x = arccos (\frac{4}{5}) + 2 πn : x = - 2 πn + \frac{π}{2} - arccos (\frac{4}{5})

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

Move

\frac{π}{2}

to the right side

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

Subtract

\frac{π}{2}

from both sides

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

Simplify

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

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

Divide both sides by

- 1

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

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Simplify

\frac{- x}{- 1} = \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

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

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1} : - 2 πn + \frac{π}{2} - arccos (\frac{4}{5})

\frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Group like terms

= \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1} + \frac{arccos ( \frac{4}{5} )}{- 1}

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

Apply the fraction rule:

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

= - \frac{2 πn}{1}

Apply rule

\frac{a}{1} = a

= - 2 πn

= - 2 πn - \frac{\frac{π}{2}}{- 1} + \frac{arccos ( \frac{4}{5} )}{- 1}

\frac{\frac{π}{2}}{- 1} = - \frac{π}{2}

\frac{\frac{π}{2}}{- 1}

Apply the fraction rule:

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

= - \frac{\frac{π}{2}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{\frac{π}{2}}{1} = \frac{π}{2}

= - \frac{π}{2}

\frac{arccos ( \frac{4}{5} )}{- 1} = - arccos (\frac{4}{5})

\frac{arccos ( \frac{4}{5} )}{- 1}

Apply the fraction rule:

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

= - \frac{arccos ( \frac{4}{5} )}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{arccos ( \frac{4}{5} )}{1} = arccos (\frac{4}{5})

= - arccos (\frac{4}{5})

= - 2 πn - (- \frac{π}{2}) - arccos (\frac{4}{5})

Apply rule

- (- a) = a

= - 2 πn + \frac{π}{2} - arccos (\frac{4}{5})

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

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

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

Solve

\frac{π}{2} - x = 2 π - arccos (\frac{4}{5}) + 2 πn : x = - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

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

Move

\frac{π}{2}

to the right side

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

Subtract

\frac{π}{2}

from both sides

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

Simplify

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

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

Divide both sides by

- 1

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

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{2 π}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Simplify

\frac{- x}{- 1} = \frac{2 π}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

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

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{2 π}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1} : - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

\frac{2 π}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Group like terms

= \frac{2 π}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1}

\frac{2 π}{- 1} = - 2 π

\frac{2 π}{- 1}

Apply the fraction rule:

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

= - \frac{2 π}{1}

Apply rule

\frac{a}{1} = a

= - 2 π

= - 2 π + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1}

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

Apply the fraction rule:

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

= - \frac{2 πn}{1}

Apply rule

\frac{a}{1} = a

= - 2 πn

= - 2 π - 2 πn - \frac{\frac{π}{2}}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1}

\frac{\frac{π}{2}}{- 1} = - \frac{π}{2}

\frac{\frac{π}{2}}{- 1}

Apply the fraction rule:

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

= - \frac{\frac{π}{2}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{\frac{π}{2}}{1} = \frac{π}{2}

= - \frac{π}{2}

\frac{arccos ( \frac{4}{5} )}{- 1} = - arccos (\frac{4}{5})

\frac{arccos ( \frac{4}{5} )}{- 1}

Apply the fraction rule:

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

= - \frac{arccos ( \frac{4}{5} )}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{arccos ( \frac{4}{5} )}{1} = arccos (\frac{4}{5})

= - arccos (\frac{4}{5})

= - 2 π - 2 πn - (- \frac{π}{2}) - (- arccos (\frac{4}{5}))

Apply rule

- (- a) = a

= - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

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

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

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

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

Show solutions in decimal form

x = - 2 πn + \frac{π}{2} - 0.64350 \dots, x = - 2 π - 2 πn + \frac{π}{2} + 0.64350 \dots

Graph

Popular Examples

6=10cos(4*o)

solvefor y,x=sin(1/2 y)

sin^2(θ)-sin(θ)=2

solvefor x,sin(x)cos(x)=0

2/3 =(sin(135))/(sin(x))

Frequently Asked Questions (FAQ)

What is the general solution for cos(pi/2-x)= 4/5 ?
The general solution for cos(pi/2-x)= 4/5 is x=-2pin+pi/2-0.64350…,x=-2pi-2pin+pi/2+0.64350…