Trigonometry Examples

$\csc (\frac{433}{10})$

Step 1

Since $43$ is a whole number, it is a full degree. Since each minute is equal to $\frac{1}{60}$ degree, multiply $18$ by $\frac{1}{60}$ . Since each second is equal to $\frac{1}{3600}$ degree, multiply $0$ by $\frac{1}{3600}$ . Add them together.

$\csc (43 + 18 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600})$

Step 2

Simplify.

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Step 2.1

Remove parentheses.

$\csc (43 + 18 \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600})$

Step 2.2

Simplify each term.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Factor $6$ out of $18$ .

$\csc (43 + 6 (3) \cdot \frac{1}{60} + 0 \cdot \frac{1}{3600})$

Step 2.2.1.2

Factor $6$ out of $60$ .

$\csc (43 + 6 \cdot 3 \cdot \frac{1}{6 \cdot 10} + 0 \cdot \frac{1}{3600})$

Step 2.2.1.3

Cancel the common factor.

$\csc (43 + 6 \cdot 3 \cdot \frac{1}{6 \cdot 10} + 0 \cdot \frac{1}{3600})$

Step 2.2.1.4

Rewrite the expression.

$\csc (43 + 3 \cdot \frac{1}{10} + 0 \cdot \frac{1}{3600})$

Step 2.2.2

Combine $3$ and $\frac{1}{10}$ .

$\csc (43 + \frac{3}{10} + 0 \cdot \frac{1}{3600})$

Step 2.2.3

Multiply $0$ by $\frac{1}{3600}$ .

$\csc (43 + \frac{3}{10} + 0)$

Step 2.3

To write $43$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\csc (43 \cdot \frac{10}{10} + \frac{3}{10} + 0)$

Step 2.4

Combine $43$ and $\frac{10}{10}$ .

$\csc (\frac{43 \cdot 10}{10} + \frac{3}{10} + 0)$

Step 2.5

Combine the numerators over the common denominator.

$\csc (\frac{43 \cdot 10 + 3}{10} + 0)$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $43$ by $10$ .

$\csc (\frac{430 + 3}{10} + 0)$

Step 2.6.2

Add $430$ and $3$ .

$\csc (\frac{433}{10} + 0)$

Step 2.7

Add $\frac{433}{10}$ and $0$ .

$\csc (\frac{433}{10})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\csc (\frac{433}{10})$

Decimal Form:

$1.45811204 \dots$