Trigonometry Examples

$\cos (5 °) = \frac{92}{y}$

Step 1

Rewrite the equation as $\frac{92}{y} = \cos (5 °)$ .

$\frac{92}{y} = \cos (5 °)$

Step 2

Evaluate $\cos (5 °)$ .

$\frac{92}{y} = 0.99619469$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$y, 1$

Step 3.2

The LCM of one and any expression is the expression.

$y$

Step 4

Multiply each term in $\frac{92}{y} = 0.99619469$ by $y$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{92}{y} = 0.99619469$ by $y$ .

$\frac{92}{y} y = 0.99619469 y$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $y$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{92}{y} y = 0.99619469 y$

Step 4.2.1.2

Rewrite the expression.

$92 = 0.99619469 y$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $0.99619469 y = 92$ .

$0.99619469 y = 92$

Step 5.2

Divide each term in $0.99619469 y = 92$ by $0.99619469$ and simplify.

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Step 5.2.1

Divide each term in $0.99619469 y = 92$ by $0.99619469$ .

$\frac{0.99619469 y}{0.99619469} = \frac{92}{0.99619469}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $0.99619469$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{0.99619469 y}{0.99619469} = \frac{92}{0.99619469}$

Step 5.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{92}{0.99619469}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $92$ by $0.99619469$ .

$y = 92.35142505$