Precalculus Examples

$3 \cos ((\frac{5 π}{4}) - \frac{π}{4}) \cdot (\frac{3}{2}) - 2$

Step 1

Simplify each term.

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Step 1.1

Combine the numerators over the common denominator.

$3 \cos (\frac{5 π - π}{4}) \cdot \frac{3}{2} - 2$

Step 1.2

Subtract $π$ from $5 π$ .

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

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Divide $π$ by $1$ .

$3 \cos (π) \cdot \frac{3}{2} - 2$

Step 1.4

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$3 (- \cos (0)) \cdot \frac{3}{2} - 2$

Step 1.5

The exact value of $\cos (0)$ is $1$ .

$3 (- 1 \cdot 1) \cdot \frac{3}{2} - 2$

Step 1.6

Multiply $3 (- 1 \cdot 1)$ .

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Step 1.6.1

Multiply $- 1$ by $1$ .

$3 \cdot - 1 \cdot \frac{3}{2} - 2$

Step 1.6.2

Multiply $3$ by $- 1$ .

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

Step 1.7

Multiply $- 3 (\frac{3}{2})$ .

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Step 1.7.1

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

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

Step 1.7.2

Multiply $- 3$ by $3$ .

$\frac{- 9}{2} - 2$

Step 1.8

Move the negative in front of the fraction.

$- \frac{9}{2} - 2$

Step 2

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

$- \frac{9}{2} - 2 \cdot \frac{2}{2}$

Step 3

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

$- \frac{9}{2} + \frac{- 2 \cdot 2}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 9 - 2 \cdot 2}{2}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 2$ by $2$ .

$\frac{- 9 - 4}{2}$

Step 5.2

Subtract $4$ from $- 9$ .

$\frac{- 13}{2}$

Step 6

Move the negative in front of the fraction.

$- \frac{13}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{13}{2}$

Decimal Form:

$- 6.5$

Mixed Number Form:

$- 6 \frac{1}{2}$