What is the general solution for solvefor y,0=x^2cos^3(y) ?

The general solution for solvefor y,0=x^2cos^3(y) is y= pi/2+2pin,y=(3pi)/2+2pin

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solvefor y,0=x^2cos^3(y)

solve for

y, 0 = x^{2} cos^{3} (y)

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

Degrees

y = 9 0^{\circ} + 36 0^{\circ} n, y = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

0 = x^{2} cos^{3} (y)

Switch sides

x^{2} cos^{3} (y) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

cos^{3} (y) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

cos (y) = 0

General solutions for

cos (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}

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

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

tan (θ) = 3

tan (\frac{7 π}{3})

1 + tan (x) = 0

tan^{2} (x) - 3 = 0

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

What is the general solution for solvefor y,0=x^2cos^3(y) ?
The general solution for solvefor y,0=x^2cos^3(y) is y= pi/2+2pin,y=(3pi)/2+2pin