solvefor x,z=sqrt(y)sin(4x)

Solution

solve for

x, z = y sin (4 x)

x = \frac{arcsin ( \frac{z}{y} )}{4} + \frac{πn}{2}, x = \frac{π}{4} + \frac{arcsin ( - \frac{z}{y} )}{4} + \frac{πn}{2}

Solution steps

z = y sin (4 x)

Switch sides

y sin (4 x) = z

Divide both sides by

y; y \neq = 0

sin (4 x) = \frac{z y}{y}; y \neq = 0

Apply trig inverse properties

4 x = arcsin (\frac{z y}{y}) + 2 πn, 4 x = π + arcsin (- \frac{z y}{y}) + 2 πn

Solve

4 x = arcsin (\frac{z y}{y}) + 2 πn : x = \frac{arcsin ( \frac{z}{y} )}{4} + \frac{πn}{2}

Solve

4 x = π + arcsin (- \frac{z y}{y}) + 2 πn : x = \frac{π}{4} + \frac{arcsin ( - \frac{z}{y} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{z}{y} )}{4} + \frac{πn}{2}, x = \frac{π}{4} + \frac{arcsin ( - \frac{z}{y} )}{4} + \frac{πn}{2}

csc (x) cot (x) = 0

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5 cos (3 x) = - 3

2 sin^{3} (x) + sin^{2} (x) = 0

2 sin^{2} (θ) = sin (θ), 0 \leq θ \leq 2 π