Trigonometry Examples

$\arccos (\frac{V}{170})$

Step 1

Select a few points to graph.

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Find the point at $x = - 170$ .

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Replace the variable $x$ with $- 170$ in the expression.

$f (- 170) = \arccos (\frac{- 170}{170})$

Simplify the result.

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Divide $- 170$ by $170$ .

$f (- 170) = \arccos (- 1)$

The exact value of $\arccos (- 1)$ is $π$ .

$f (- 170) = π$

The final answer is $π$ .

$π$

Find the point at $x = - 85$ .

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Replace the variable $x$ with $- 85$ in the expression.

$f (- 85) = \arccos (\frac{- 85}{170})$

Simplify the result.

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Cancel the common factor of $- 85$ and $170$ .

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Factor $85$ out of $- 85$ .

$f (- 85) = \arccos (\frac{85 (- 1)}{170})$

Cancel the common factors.

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Factor $85$ out of $170$ .

$f (- 85) = \arccos (\frac{85 \cdot - 1}{85 \cdot 2})$

Cancel the common factor.

$f (- 85) = \arccos (\frac{85 \cdot - 1}{85 \cdot 2})$

Rewrite the expression.

$f (- 85) = \arccos (\frac{- 1}{2})$

Move the negative in front of the fraction.

$f (- 85) = \arccos (- \frac{1}{2})$

The exact value of $\arccos (- \frac{1}{2})$ is $\frac{2 π}{3}$ .

$f (- 85) = \frac{2 π}{3}$

The final answer is $\frac{2 π}{3}$ .

$\frac{2 π}{3}$

Find the point at $x = 0$ .

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Replace the variable $x$ with $0$ in the expression.

$f (0) = \arccos (\frac{0}{170})$

Simplify the result.

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Divide $0$ by $170$ .

$f (0) = \arccos (0)$

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

$f (0) = \frac{π}{2}$

The final answer is $\frac{π}{2}$ .

$\frac{π}{2}$

Find the point at $x = 85$ .

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Replace the variable $x$ with $85$ in the expression.

$f (85) = \arccos (\frac{85}{170})$

Simplify the result.

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Cancel the common factor of $85$ and $170$ .

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Factor $85$ out of $85$ .

$f (85) = \arccos (\frac{85 (1)}{170})$

Cancel the common factors.

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Factor $85$ out of $170$ .

$f (85) = \arccos (\frac{85 \cdot 1}{85 \cdot 2})$

Cancel the common factor.

$f (85) = \arccos (\frac{85 \cdot 1}{85 \cdot 2})$

Rewrite the expression.

$f (85) = \arccos (\frac{1}{2})$

The exact value of $\arccos (\frac{1}{2})$ is $\frac{π}{3}$ .

$f (85) = \frac{π}{3}$

The final answer is $\frac{π}{3}$ .

$\frac{π}{3}$

Find the point at $x = 170$ .

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Replace the variable $x$ with $170$ in the expression.

$f (170) = \arccos (\frac{170}{170})$

Simplify the result.

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Divide $170$ by $170$ .

$f (170) = \arccos (1)$

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

$f (170) = 0$

The final answer is $0$ .

$0$

List the points in a table.

$\begin{array}{c} x & f (x) \\ - 170 & π \\ - 85 & \frac{2 π}{3} \\ 0 & \frac{π}{2} \\ 85 & \frac{π}{3} \\ 170 & 0 \end{array}$

Step 2

The trig function can be graphed using the points.

$\begin{array}{c} x & f (x) \\ - 170 & π \\ - 85 & \frac{2 π}{3} \\ 0 & \frac{π}{2} \\ 85 & \frac{π}{3} \\ 170 & 0 \end{array}$

Step 3