Calculus Examples

$\tan (\frac{π}{5} - \frac{π}{3})$

Step 1

To write $\frac{π}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\tan (\frac{π}{5} \cdot \frac{3}{3} - \frac{π}{3})$

Step 2

To write $- \frac{π}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\tan (\frac{π}{5} \cdot \frac{3}{3} - \frac{π}{3} \cdot \frac{5}{5})$

Step 3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{π}{5}$ by $\frac{3}{3}$ .

$\tan (\frac{π \cdot 3}{5 \cdot 3} - \frac{π}{3} \cdot \frac{5}{5})$

Step 3.2

Multiply $5$ by $3$ .

$\tan (\frac{π \cdot 3}{15} - \frac{π}{3} \cdot \frac{5}{5})$

Step 3.3

Multiply $\frac{π}{3}$ by $\frac{5}{5}$ .

$\tan (\frac{π \cdot 3}{15} - \frac{π \cdot 5}{3 \cdot 5})$

Step 3.4

Multiply $3$ by $5$ .

$\tan (\frac{π \cdot 3}{15} - \frac{π \cdot 5}{15})$

Step 4

Combine the numerators over the common denominator.

$\tan (\frac{π \cdot 3 - π \cdot 5}{15})$

Step 5

Simplify the numerator.

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Step 5.1

Move $3$ to the left of $π$ .

$\tan (\frac{3 \cdot π - π \cdot 5}{15})$

Step 5.2

Multiply $5$ by $- 1$ .

$\tan (\frac{3 π - 5 π}{15})$

Step 5.3

Subtract $5 π$ from $3 π$ .

$\tan (\frac{- 2 π}{15})$

Step 6

Move the negative in front of the fraction.

$\tan (- \frac{2 π}{15})$

Step 7

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\tan (\frac{28 π}{15})$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\tan (\frac{28 π}{15})$

Decimal Form:

$- 0.44522868 \dots$