Calculus Examples

$3 \sin (\frac{π}{4}) - 4 \cos (\frac{π}{4})$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$3 \frac{\sqrt{2}}{2} - 4 \cos (\frac{π}{4})$

Step 1.2

Combine $3$ and $\frac{\sqrt{2}}{2}$ .

$\frac{3 \sqrt{2}}{2} - 4 \cos (\frac{π}{4})$

Step 1.3

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{3 \sqrt{2}}{2} - 4 \frac{\sqrt{2}}{2}$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $- 4$ .

$\frac{3 \sqrt{2}}{2} + 2 (- 2) \frac{\sqrt{2}}{2}$

Step 1.4.2

Cancel the common factor.

$\frac{3 \sqrt{2}}{2} + 2 \cdot - 2 \frac{\sqrt{2}}{2}$

Step 1.4.3

Rewrite the expression.

$\frac{3 \sqrt{2}}{2} - 2 \sqrt{2}$

Step 2

To write $- 2 \sqrt{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 \sqrt{2}}{2} - 2 \sqrt{2} \cdot \frac{2}{2}$

Step 3

Combine fractions.

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Step 3.1

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

$\frac{3 \sqrt{2}}{2} + \frac{- 2 \sqrt{2} \cdot 2}{2}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3 \sqrt{2} - 2 \sqrt{2} \cdot 2}{2}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $2$ by $- 2$ .

$\frac{3 \sqrt{2} - 4 \sqrt{2}}{2}$

Step 4.2

Subtract $4 \sqrt{2}$ from $3 \sqrt{2}$ .

$\frac{- \sqrt{2}}{2}$

Step 5

Move the negative in front of the fraction.

$- \frac{\sqrt{2}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{2}}{2}$

Decimal Form:

$- 0.70710678 \dots$