What is the general solution for cos(piy)=0 ?

The general solution for cos(piy)=0 is y= 1/2+2n,y= 3/2+2n

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cos(piy)=0

Solution

cos (π y) = 0

Solution

y = \frac{1}{2} + 2 n, y = \frac{3}{2} + 2 n

Degrees

y = 28.64788 \dots^{\circ} + 114.59155 \dots^{\circ} n, y = 85.94366 \dots^{\circ} + 114.59155 \dots^{\circ} n

Solution steps

cos (π y) = 0

General solutions for

cos (π y) = 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}

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

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

Solve

π y = \frac{π}{2} + 2 πn : y = \frac{1}{2} + 2 n

π y = \frac{π}{2} + 2 πn

Divide both sides by

π

π y = \frac{π}{2} + 2 πn

Divide both sides by

π

\frac{π y}{π} = \frac{\frac{π}{2}}{π} + \frac{2 πn}{π}

Simplify

\frac{π y}{π} = \frac{\frac{π}{2}}{π} + \frac{2 πn}{π}

Simplify

\frac{π y}{π} : y

\frac{π y}{π}

Cancel the common factor:

π

= y

Simplify

\frac{\frac{π}{2}}{π} + \frac{2 πn}{π} : \frac{1}{2} + 2 n

\frac{\frac{π}{2}}{π} + \frac{2 πn}{π}

\frac{\frac{π}{2}}{π} = \frac{1}{2}

\frac{\frac{π}{2}}{π}

Apply the fraction rule:

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

= \frac{π}{2 π}

Cancel the common factor:

π

= \frac{1}{2}

\frac{2 πn}{π} = 2 n

\frac{2 πn}{π}

Cancel the common factor:

π

= 2 n

= \frac{1}{2} + 2 n

y = \frac{1}{2} + 2 n

y = \frac{1}{2} + 2 n

y = \frac{1}{2} + 2 n

Solve

π y = \frac{3 π}{2} + 2 πn : y = \frac{3}{2} + 2 n

π y = \frac{3 π}{2} + 2 πn

Divide both sides by

π

π y = \frac{3 π}{2} + 2 πn

Divide both sides by

π

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

Simplify

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

Simplify

\frac{π y}{π} : y

\frac{π y}{π}

Cancel the common factor:

π

= y

Simplify

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

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

\frac{\frac{3 π}{2}}{π} = \frac{3}{2}

\frac{\frac{3 π}{2}}{π}

Apply the fraction rule:

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

= \frac{3 π}{2 π}

Cancel the common factor:

π

= \frac{3}{2}

\frac{2 πn}{π} = 2 n

\frac{2 πn}{π}

Cancel the common factor:

π

= 2 n

= \frac{3}{2} + 2 n

y = \frac{3}{2} + 2 n

y = \frac{3}{2} + 2 n

y = \frac{3}{2} + 2 n

y = \frac{1}{2} + 2 n, y = \frac{3}{2} + 2 n

Popular Examples

cos(t)=-1/3

cos (t) = - \frac{1}{3}

sqrt(3)cot(x)-1=0,0<= x<= 2pix

3 cot (x) - 1 = 0, 0 \leq x \leq 2 π x

1=cosh(x)

1 = cosh (x)

solvefor x,cos^2(x)= 1/2 solve for

x, cos^{2} (x) = \frac{1}{2}

(sqrt(3))/3 =tan(x)

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

Frequently Asked Questions (FAQ)

What is the general solution for cos(piy)=0 ?
The general solution for cos(piy)=0 is y= 1/2+2n,y= 3/2+2n