Trigonometry Examples

$h = - 4 \cos (\frac{π}{6} \cdot 16 - \frac{2 π}{3}) + 6$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $2$ .

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Step 1.1.1.1

Factor $2$ out of $6$ .

$h = - 4 \cos (\frac{π}{2 (3)} \cdot 16 - \frac{2 π}{3}) + 6$

Step 1.1.1.2

Factor $2$ out of $16$ .

$h = - 4 \cos (\frac{π}{2 \cdot 3} \cdot (2 \cdot 8) - \frac{2 π}{3}) + 6$

Step 1.1.1.3

Cancel the common factor.

$h = - 4 \cos (\frac{π}{2 \cdot 3} \cdot (2 \cdot 8) - \frac{2 π}{3}) + 6$

Step 1.1.1.4

Rewrite the expression.

$h = - 4 \cos (\frac{π}{3} \cdot 8 - \frac{2 π}{3}) + 6$

Step 1.1.2

Combine $\frac{π}{3}$ and $8$ .

$h = - 4 \cos (\frac{π \cdot 8}{3} - \frac{2 π}{3}) + 6$

Step 1.1.3

Move $8$ to the left of $π$ .

$h = - 4 \cos (\frac{8 π}{3} - \frac{2 π}{3}) + 6$

Step 1.2

Combine the numerators over the common denominator.

$h = - 4 \cos (\frac{8 π - 2 π}{3}) + 6$

Step 1.3

Subtract $2 π$ from $8 π$ .

$h = - 4 \cos (\frac{6 π}{3}) + 6$

Step 1.4

Cancel the common factor of $6$ and $3$ .

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Step 1.4.1

Factor $3$ out of $6 π$ .

$h = - 4 \cos (\frac{3 (2 π)}{3}) + 6$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $3$ out of $3$ .

$h = - 4 \cos (\frac{3 (2 π)}{3 (1)}) + 6$

Step 1.4.2.2

Cancel the common factor.

$h = - 4 \cos (\frac{3 (2 π)}{3 \cdot 1}) + 6$

Step 1.4.2.3

Rewrite the expression.

$h = - 4 \cos (\frac{2 π}{1}) + 6$

Step 1.4.2.4

Divide $2 π$ by $1$ .

$h = - 4 \cos (2 π) + 6$

Step 1.5

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

$h = - 4 \cos (0) + 6$

Step 1.6

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

$h = - 4 \cdot 1 + 6$

Step 1.7

Multiply $- 4$ by $1$ .

$h = - 4 + 6$

Step 2

Add $- 4$ and $6$ .

$h = 2$