Trigonometry Examples

$\frac{6}{5} \cdot \arccos (\frac{y}{8}) = π$

Step 1

Subtract $π$ from both sides of the equation.

$\frac{6}{5} \cdot \arccos (\frac{y}{8}) - π = 0$

Step 2

Combine $\frac{6}{5}$ and $\arccos (\frac{y}{8})$ .

$\frac{6 \arccos (\frac{y}{8})}{5} - π = 0$

Step 3

Set the argument in $\arccos (\frac{y}{8})$ less than $- 1$ to find where the expression is undefined.

$\frac{y}{8} < - 1$

Step 4

Solve for $y$ .

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Step 4.1

Multiply both sides by $8$ .

$\frac{y}{8} \cdot 8 < - 1 \cdot 8$

Step 4.2

Simplify.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Cancel the common factor of $8$ .

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Step 4.2.1.1.1

Cancel the common factor.

$\frac{y}{8} \cdot 8 < - 1 \cdot 8$

Step 4.2.1.1.2

Rewrite the expression.

$y < - 1 \cdot 8$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Multiply $- 1$ by $8$ .

$y < - 8$

Step 5

Set the argument in $\arccos (\frac{y}{8})$ greater than $1$ to find where the expression is undefined.

$\frac{y}{8} > 1$

Step 6

Solve for $y$ .

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Step 6.1

Multiply both sides by $8$ .

$\frac{y}{8} \cdot 8 > 1 \cdot 8$

Step 6.2

Simplify.

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Step 6.2.1

Simplify the left side.

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Step 6.2.1.1

Cancel the common factor of $8$ .

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Step 6.2.1.1.1

Cancel the common factor.

$\frac{y}{8} \cdot 8 > 1 \cdot 8$

Step 6.2.1.1.2

Rewrite the expression.

$y > 1 \cdot 8$

Step 6.2.2

Simplify the right side.

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Step 6.2.2.1

Multiply $8$ by $1$ .

$y > 8$

Step 7

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$y < - 8, y > 8$

$(- \infty, - 8) \cup (8, \infty)$

Step 8