What is the general solution for cos(pi/2+x)=0 ?

The general solution for cos(pi/2+x)=0 is x=2pin,x=2pin+pi

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cos(pi/2+x)=0

Solution

cos (\frac{π}{2} + x) = 0

Solution

x = 2 πn, x = 2 πn + π

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

cos (\frac{π}{2} + x) = 0

General solutions for

cos (\frac{π}{2} + x) = 0

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

\frac{π}{2} + x = \frac{π}{2} + 2 πn, \frac{π}{2} + x = \frac{3 π}{2} + 2 πn

\frac{π}{2} + x = \frac{π}{2} + 2 πn, \frac{π}{2} + x = \frac{3 π}{2} + 2 πn

Solve

\frac{π}{2} + x = \frac{π}{2} + 2 πn : x = 2 πn

\frac{π}{2} + x = \frac{π}{2} + 2 πn

Subtract

\frac{π}{2}

from both sides

\frac{π}{2} + x - \frac{π}{2} = \frac{π}{2} + 2 πn - \frac{π}{2}

Simplify

x = 2 πn

Solve

\frac{π}{2} + x = \frac{3 π}{2} + 2 πn : x = 2 πn + π

\frac{π}{2} + x = \frac{3 π}{2} + 2 πn

Move

\frac{π}{2}

to the right side

\frac{π}{2} + x = \frac{3 π}{2} + 2 πn

Subtract

\frac{π}{2}

from both sides

\frac{π}{2} + x - \frac{π}{2} = \frac{3 π}{2} + 2 πn - \frac{π}{2}

Simplify

\frac{π}{2} + x - \frac{π}{2} = \frac{3 π}{2} + 2 πn - \frac{π}{2}

Simplify

\frac{π}{2} + x - \frac{π}{2} : x

\frac{π}{2} + x - \frac{π}{2}

Add similar elements:

\frac{π}{2} - \frac{π}{2} = 0

= x

Simplify

\frac{3 π}{2} + 2 πn - \frac{π}{2} : 2 πn + π

\frac{3 π}{2} + 2 πn - \frac{π}{2}

Group like terms

= 2 πn - \frac{π}{2} + \frac{3 π}{2}

Combine the fractions

- \frac{π}{2} + \frac{3 π}{2} : π

Apply rule

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

= \frac{- π + 3 π}{2}

Add similar elements:

- π + 3 π = 2 π

= \frac{2 π}{2}

Divide the numbers:

\frac{2}{2} = 1

= π

= 2 πn + π

x = 2 πn + π

x = 2 πn + π

x = 2 πn + π

x = 2 πn, x = 2 πn + π

Popular Examples

4.1=4.2cos(18t)+3

4.1 = 4.2 cos (18 t) + 3

4sin(x)-13=2cos^2(x)-9

4 sin (x) - 13 = 2 cos^{2} (x) - 9

cos(θ)=-8/11

cos (θ) = - \frac{8}{11}

sin(θ)=(sqrt(3))/(12)

sin (θ) = \frac{3}{12}

cos(x)= 12/17

cos (x) = \frac{12}{17}

Frequently Asked Questions (FAQ)

What is the general solution for cos(pi/2+x)=0 ?
The general solution for cos(pi/2+x)=0 is x=2pin,x=2pin+pi