Precalculus Examples

$\cos (112) \cos (45) + \sin (112) \sin (45)$

Step 1

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

$\cos (112) \frac{\sqrt{2}}{2} + \sin (112) \sin (45)$

Step 2

Combine $\cos (112)$ and $\frac{\sqrt{2}}{2}$ .

$\frac{\cos (112) \sqrt{2}}{2} + \sin (112) \sin (45)$

Step 3

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

$\frac{\cos (112) \sqrt{2}}{2} + \sin (112) \frac{\sqrt{2}}{2}$

Step 4

Combine $\sin (112)$ and $\frac{\sqrt{2}}{2}$ .

$\frac{\cos (112) \sqrt{2}}{2} + \frac{\sin (112) \sqrt{2}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\cos (112) \sqrt{2}}{2} + \frac{\sin (112) \sqrt{2}}{2}$

Decimal Form:

$0.39073112 \dots$