Trigonometry Examples

$r = \frac{3}{\cos (x)}$

Step 1

Rewrite the equation as $\frac{3}{\cos (x)} = r$ .

$\frac{3}{\cos (x)} = r$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$\cos (x), 1$

Step 2.2

The LCM of one and any expression is the expression.

$\cos (x)$

Step 3

Multiply each term in $\frac{3}{\cos (x)} = r$ by $\cos (x)$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{3}{\cos (x)} = r$ by $\cos (x)$ .

$\frac{3}{\cos (x)} \cos (x) = r \cos (x)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $\cos (x)$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3}{\cos (x)} \cos (x) = r \cos (x)$

Step 3.2.1.2

Rewrite the expression.

$3 = r \cos (x)$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $r \cos (x) = 3$ .

$r \cos (x) = 3$

Step 4.2

Divide each term in $r \cos (x) = 3$ by $r$ and simplify.

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Step 4.2.1

Divide each term in $r \cos (x) = 3$ by $r$ .

$\frac{r \cos (x)}{r} = \frac{3}{r}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $r$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{r \cos (x)}{r} = \frac{3}{r}$

Step 4.2.2.1.2

Divide $\cos (x)$ by $1$ .

$\cos (x) = \frac{3}{r}$

Step 5

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

$x = \arccos (\frac{3}{r})$