Trigonometry Examples

$y = 0.35 \cos (8 (x - \frac{π}{4}))$

Step 1

Rewrite the equation as $0.35 \cos (8 (x - \frac{π}{4})) = y$ .

$0.35 \cos (8 (x - \frac{π}{4})) = y$

Step 2

Divide each term in $0.35 \cos (8 (x - \frac{π}{4})) = y$ by $0.35$ and simplify.

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Step 2.1

Divide each term in $0.35 \cos (8 (x - \frac{π}{4})) = y$ by $0.35$ .

$\frac{0.35 \cos (8 (x - \frac{π}{4}))}{0.35} = \frac{y}{0.35}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $0.35$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{0.35 \cos (8 (x - \frac{π}{4}))}{0.35} = \frac{y}{0.35}$

Step 2.2.1.2

Divide $\cos (8 (x - \frac{π}{4}))$ by $1$ .

$\cos (8 (x - \frac{π}{4})) = \frac{y}{0.35}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply by $1$ .

$\cos (8 (x - \frac{π}{4})) = \frac{1 y}{0.35}$

Step 2.3.2

Factor $0.35$ out of $0.35$ .

$\cos (8 (x - \frac{π}{4})) = \frac{1 y}{0.35 (1)}$

Step 2.3.3

Separate fractions.

$\cos (8 (x - \frac{π}{4})) = \frac{1}{0.35} \cdot \frac{y}{1}$

Step 2.3.4

Divide $1$ by $0.35$ .

$\cos (8 (x - \frac{π}{4})) = 2.\overline{857142} \frac{y}{1}$

Step 2.3.5

Divide $y$ by $1$ .

$\cos (8 (x - \frac{π}{4})) = 2.\overline{857142} y$

Step 3

Take the inverse cosine of both sides of the equation to extract $x$ from inside the cosine.

$8 (x - \frac{π}{4}) = \arccos (2.\overline{857142} y)$

Step 4

Simplify the left side.

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Step 4.1

Simplify $8 (x - \frac{π}{4})$ .

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Step 4.1.1

Apply the distributive property.

$8 x + 8 (- \frac{π}{4}) = \arccos (2.\overline{857142} y)$

Step 4.1.2

Cancel the common factor of $4$ .

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Step 4.1.2.1

Move the leading negative in $- \frac{π}{4}$ into the numerator.

$8 x + 8 \frac{- π}{4} = \arccos (2.\overline{857142} y)$

Step 4.1.2.2

Factor $4$ out of $8$ .

$8 x + 4 (2) \frac{- π}{4} = \arccos (2.\overline{857142} y)$

Step 4.1.2.3

Cancel the common factor.

$8 x + 4 \cdot 2 \frac{- π}{4} = \arccos (2.\overline{857142} y)$

Step 4.1.2.4

Rewrite the expression.

$8 x + 2 (- π) = \arccos (2.\overline{857142} y)$

Step 4.1.3

Multiply $- 1$ by $2$ .

$8 x - 2 π = \arccos (2.\overline{857142} y)$

Step 5

Add $2 π$ to both sides of the equation.

$8 x = \arccos (2.\overline{857142} y) + 2 π$

Step 6

Divide each term in $8 x = \arccos (2.\overline{857142} y) + 2 π$ by $8$ and simplify.

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Step 6.1

Divide each term in $8 x = \arccos (2.\overline{857142} y) + 2 π$ by $8$ .

$\frac{8 x}{8} = \frac{\arccos (2.\overline{857142} y)}{8} + \frac{2 π}{8}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $8$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{\arccos (2.\overline{857142} y)}{8} + \frac{2 π}{8}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{\arccos (2.\overline{857142} y)}{8} + \frac{2 π}{8}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of $2$ and $8$ .

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Step 6.3.1.1

Factor $2$ out of $2 π$ .

$x = \frac{\arccos (2.\overline{857142} y)}{8} + \frac{2 (π)}{8}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor $2$ out of $8$ .

$x = \frac{\arccos (2.\overline{857142} y)}{8} + \frac{2 π}{2 \cdot 4}$

Step 6.3.1.2.2

Cancel the common factor.

$x = \frac{\arccos (2.\overline{857142} y)}{8} + \frac{2 π}{2 \cdot 4}$

Step 6.3.1.2.3

Rewrite the expression.

$x = \frac{\arccos (2.\overline{857142} y)}{8} + \frac{π}{4}$