Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Evaluate $\cos (112)$ .

$- 0.37460659 \cos (45) + \sin (112) \sin (45)$

Step 1.2

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

$- 0.37460659 \frac{\sqrt{2}}{2} + \sin (112) \sin (45)$

Step 1.3

Multiply $- 0.37460659 \frac{\sqrt{2}}{2}$ .

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Step 1.3.1

Combine $- 0.37460659$ and $\frac{\sqrt{2}}{2}$ .

$\frac{- 0.37460659 \sqrt{2}}{2} + \sin (112) \sin (45)$

Step 1.3.2

Multiply $- 0.37460659$ by $\sqrt{2}$ .

$\frac{- 0.52977372}{2} + \sin (112) \sin (45)$

Step 1.4

Divide $- 0.52977372$ by $2$ .

$- 0.26488686 + \sin (112) \sin (45)$

Step 1.5

Evaluate $\sin (112)$ .

$- 0.26488686 + 0.92718385 \sin (45)$

Step 1.6

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

$- 0.26488686 + 0.92718385 \frac{\sqrt{2}}{2}$

Step 1.7

Multiply $0.92718385 \frac{\sqrt{2}}{2}$ .

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Step 1.7.1

Combine $0.92718385$ and $\frac{\sqrt{2}}{2}$ .

$- 0.26488686 + \frac{0.92718385 \sqrt{2}}{2}$

Step 1.7.2

Multiply $0.92718385$ by $\sqrt{2}$ .

$- 0.26488686 + \frac{1.31123598}{2}$

Step 1.8

Divide $1.31123598$ by $2$ .

$- 0.26488686 + 0.65561799$

Step 2

Add $- 0.26488686$ and $0.65561799$ .

$0.39073112$