Trigonometry Examples

$\cot (42) \csc (48) - \sin (42)$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\cot (42)$ in terms of sines and cosines.

$\frac{\cos (42)}{\sin (42)} \csc (48) - \sin (42)$

Step 1.2

Rewrite $\csc (48)$ in terms of sines and cosines.

$\frac{\cos (42)}{\sin (42)} \cdot \frac{1}{\sin (48)} - \sin (42)$

Step 1.3

Multiply $\frac{\cos (42)}{\sin (42)}$ by $\frac{1}{\sin (48)}$ .

$\frac{\cos (42)}{\sin (42) \sin (48)} - \sin (42)$

Step 2

Simplify each term.

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Step 2.1

Separate fractions.

$\frac{1}{\sin (48)} \cdot \frac{\cos (42)}{\sin (42)} - \sin (42)$

Step 2.2

Convert from $\frac{\cos (42)}{\sin (42)}$ to $\cot (42)$ .

$\frac{1}{\sin (48)} \cot (42) - \sin (42)$

Step 2.3

Convert from $\frac{1}{\sin (48)}$ to $\csc (48)$ .

$\csc (48) \cot (42) - \sin (42)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\csc (48) \cot (42) - \sin (42)$

Decimal Form:

$0.82534594 \dots$