Trigonometry Examples

$\frac{\sin (45)}{\cos (65)}$

Step 1

Rewrite $\frac{\sin (45)}{\cos (65)}$ as a product.

$\sin (45) \frac{1}{\cos (65)}$

Step 2

Write $\sin (45)$ as a fraction with denominator $1$ .

$\frac{\sin (45)}{1} \cdot \frac{1}{\cos (65)}$

Step 3

Simplify.

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Step 3.1

Divide $\sin (45)$ by $1$ .

$\sin (45) \frac{1}{\cos (65)}$

Step 3.2

Convert from $\frac{1}{\cos (65)}$ to $\sec (65)$ .

$\sin (45) \sec (65)$

Step 4

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} \sec (65)$

Step 5

Combine $\frac{\sqrt{2}}{2}$ and $\sec (65)$ .

$\frac{\sqrt{2} \sec (65)}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{2} \sec (65)}{2}$

Decimal Form:

$1.67315718 \dots$