Trigonometry Examples

$\frac{5 π}{3} - \frac{2}{π}$

Step 1

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

$\frac{5 π}{3} \cdot \frac{π}{π} - \frac{2}{π}$

Step 2

To write $- \frac{2}{π}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 π}{3} \cdot \frac{π}{π} - \frac{2}{π} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $3 π$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{5 π π}{3 π} - \frac{2}{π} \cdot \frac{3}{3}$

Step 3.2

Multiply $\frac{2}{π}$ by $\frac{3}{3}$ .

$\frac{5 π π}{3 π} - \frac{2 \cdot 3}{π \cdot 3}$

Step 3.3

Reorder the factors of $π \cdot 3$ .

$\frac{5 π π}{3 π} - \frac{2 \cdot 3}{3 π}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 π π - 2 \cdot 3}{3 π}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5 π π$ .

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Step 5.1.1

Raise $π$ to the power of $1$ .

$\frac{5 (π^{1} π) - 2 \cdot 3}{3 π}$

Step 5.1.2

Raise $π$ to the power of $1$ .

$\frac{5 (π^{1} π^{1}) - 2 \cdot 3}{3 π}$

Step 5.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 π^{1 + 1} - 2 \cdot 3}{3 π}$

Step 5.1.4

Add $1$ and $1$ .

$\frac{5 π^{2} - 2 \cdot 3}{3 π}$

Step 5.2

Multiply $- 2$ by $3$ .

$\frac{5 π^{2} - 6}{3 π}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5 π^{2} - 6}{3 π}$

Decimal Form:

$4.59936798 \dots$