Trigonometry Examples

$\cot (13) \cdot \csc (77) \cdot \sin (13)$

Step 1

Rewrite $\cot (13)$ in terms of sines and cosines.

$\frac{\cos (13)}{\sin (13)} \cdot \csc (77) \cdot \sin (13)$

Step 2

Rewrite $\csc (77)$ in terms of sines and cosines.

$\frac{\cos (13)}{\sin (13)} \cdot \frac{1}{\sin (77)} \cdot \sin (13)$

Step 3

Multiply $\frac{\cos (13)}{\sin (13)}$ by $\frac{1}{\sin (77)}$ .

$\frac{\cos (13)}{\sin (13) \sin (77)} \cdot \sin (13)$

Step 4

Cancel the common factor of $\sin (13)$ .

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Step 4.1

Factor $\sin (13)$ out of $\sin (13) \sin (77)$ .

$\frac{\cos (13)}{\sin (13) (\sin (77))} \cdot \sin (13)$

Step 4.2

Cancel the common factor.

$\frac{\cos (13)}{\sin (13) \sin (77)} \cdot \sin (13)$

Step 4.3

Rewrite the expression.

$\frac{\cos (13)}{\sin (77)}$

Step 5

Rewrite $\frac{\cos (13)}{\sin (77)}$ as a product.

$\cos (13) \frac{1}{\sin (77)}$

Step 6

Write $\cos (13)$ as a fraction with denominator $1$ .

$\frac{\cos (13)}{1} \cdot \frac{1}{\sin (77)}$

Step 7

Simplify.

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Step 7.1

Divide $\cos (13)$ by $1$ .

$\cos (13) \frac{1}{\sin (77)}$

Step 7.2

Convert from $\frac{1}{\sin (77)}$ to $\csc (77)$ .

$\cos (13) \csc (77)$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\cos (13) \csc (77)$

Decimal Form:

$1.000000000000 \dots$