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Popular >

solvefor x,y=5cos(8x)-y

Solution

solve for

x, y = 5 cos (8 x) - y

Solution

x = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}, x = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

Solution steps

y = 5 cos (8 x) - y

Switch sides

5 cos (8 x) - y = y

Move

y

to the right side

5 cos (8 x) - y = y

Add

y

to both sides

5 cos (8 x) - y + y = y + y

Simplify

5 cos (8 x) = 2 y

5 cos (8 x) = 2 y

Divide both sides by

5

5 cos (8 x) = 2 y

Divide both sides by

5

\frac{5 cos ( 8 x )}{5} = \frac{2 y}{5}

Simplify

cos (8 x) = \frac{2 y}{5}

cos (8 x) = \frac{2 y}{5}

Apply trig inverse properties

cos (8 x) = \frac{2 y}{5}

General solutions for

cos (8 x) = \frac{2 y}{5}

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

8 x = arccos (\frac{2 y}{5}) + 2 πn, 8 x = - arccos (\frac{2 y}{5}) + 2 πn

8 x = arccos (\frac{2 y}{5}) + 2 πn, 8 x = - arccos (\frac{2 y}{5}) + 2 πn

Solve

8 x = arccos (\frac{2 y}{5}) + 2 πn : x = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

8 x = arccos (\frac{2 y}{5}) + 2 πn

Divide both sides by

8

8 x = arccos (\frac{2 y}{5}) + 2 πn

Divide both sides by

8

\frac{8 x}{8} = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{2 πn}{8}

Simplify

x = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

x = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

Solve

8 x = - arccos (\frac{2 y}{5}) + 2 πn : x = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

8 x = - arccos (\frac{2 y}{5}) + 2 πn

Divide both sides by

8

8 x = - arccos (\frac{2 y}{5}) + 2 πn

Divide both sides by

8

\frac{8 x}{8} = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{2 πn}{8}

Simplify

x = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

x = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

x = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}, x = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

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