Precalculus Examples

$y = - 3 \cos (\frac{6 π}{12} - π)$

Step 1

Cancel the common factor of $6$ and $12$ .

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Step 1.1

Factor $6$ out of $6 π$ .

$y = - 3 \cos (\frac{6 (π)}{12} - π)$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $6$ out of $12$ .

$y = - 3 \cos (\frac{6 π}{6 \cdot 2} - π)$

Step 1.2.2

Cancel the common factor.

$y = - 3 \cos (\frac{6 π}{6 \cdot 2} - π)$

Step 1.2.3

Rewrite the expression.

$y = - 3 \cos (\frac{π}{2} - π)$

Step 2

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

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

Step 3

Combine fractions.

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Step 3.1

Combine $- π$ and $\frac{2}{2}$ .

$y = - 3 \cos (\frac{π}{2} + \frac{- π \cdot 2}{2})$

Step 3.2

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Multiply $2$ by $- 1$ .

$y = - 3 \cos (\frac{π - 2 π}{2})$

Step 4.2

Subtract $2 π$ from $π$ .

$y = - 3 \cos (\frac{- π}{2})$

Step 5

Move the negative in front of the fraction.

$y = - 3 \cos (- \frac{π}{2})$

Step 6

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$y = - 3 \cos (\frac{3 π}{2})$

Step 7

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$y = - 3 \cos (\frac{π}{2})$

Step 8

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$y = - 3 \cdot 0$

Step 9

Multiply $- 3$ by $0$ .

$y = 0$