Trigonometry Examples

$3 \cdot \arccos (x) - 2.75$

Step 1

Select a few points to graph.

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Step 1.1

Find the point at $x = - 1$ .

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Step 1.1.1

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = 3 \cdot \arccos (- 1) - 2.75$

Step 1.1.2

Simplify the result.

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Step 1.1.2.1

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

$f (- 1) = 3 π - 2.75$

Step 1.1.2.2

Subtract $2.75$ from $3 π$ .

$f (- 1) = 6.67477796$

Step 1.1.2.3

The final answer is $6.67477796$ .

$6.67477796$

Step 1.2

Find the point at $x = - \frac{1}{2}$ .

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Step 1.2.1

Replace the variable $x$ with $- \frac{1}{2}$ in the expression.

$f (- \frac{1}{2}) = 3 \cdot \arccos (- \frac{1}{2}) - 2.75$

Step 1.2.2

Simplify the result.

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Step 1.2.2.1

Simplify each term.

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Step 1.2.2.1.1

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

$f (- \frac{1}{2}) = 3 \cdot \frac{2 π}{3} - 2.75$

Step 1.2.2.1.2

Cancel the common factor of $3$ .

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Step 1.2.2.1.2.1

Cancel the common factor.

$f (- \frac{1}{2}) = 3 \cdot \frac{2 π}{3} - 2.75$

Step 1.2.2.1.2.2

Rewrite the expression.

$f (- \frac{1}{2}) = 2 π - 2.75$

Step 1.2.2.2

Subtract $2.75$ from $2 π$ .

$f (- \frac{1}{2}) = 3.5331853$

Step 1.2.2.3

The final answer is $3.5331853$ .

$3.5331853$

Step 1.3

Find the point at $x = 0$ .

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Step 1.3.1

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

$f (0) = 3 \cdot \arccos (0) - 2.75$

Step 1.3.2

Simplify the result.

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Step 1.3.2.1

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

$f (0) = \frac{3 π}{2} - 2.75$

Step 1.3.2.2

Subtract $2.75$ from $\frac{3 π}{2}$ .

$f (0) = 1.96238898$

Step 1.3.2.3

The final answer is $1.96238898$ .

$1.96238898$

Step 1.4

Find the point at $x = \frac{1}{2}$ .

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Step 1.4.1

Replace the variable $x$ with $\frac{1}{2}$ in the expression.

$f (\frac{1}{2}) = 3 \cdot \arccos (\frac{1}{2}) - 2.75$

Step 1.4.2

Simplify the result.

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Step 1.4.2.1

Simplify each term.

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Step 1.4.2.1.1

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

$f (\frac{1}{2}) = 3 \cdot \frac{π}{3} - 2.75$

Step 1.4.2.1.2

Cancel the common factor of $3$ .

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Step 1.4.2.1.2.1

Cancel the common factor.

$f (\frac{1}{2}) = 3 \cdot \frac{π}{3} - 2.75$

Step 1.4.2.1.2.2

Rewrite the expression.

$f (\frac{1}{2}) = π - 2.75$

Step 1.4.2.2

Replace with decimal approximation.

$f (\frac{1}{2}) = 3.14159265 - 2.75$

Step 1.4.2.3

Subtract $2.75$ from $3.14159265$ .

$f (\frac{1}{2}) = 0.39159265$

Step 1.4.2.4

The final answer is $0.39159265$ .

$0.39159265$

Step 1.5

Find the point at $x = 1$ .

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Step 1.5.1

Replace the variable $x$ with $1$ in the expression.

$f (1) = 3 \cdot \arccos (1) - 2.75$

Step 1.5.2

Simplify the result.

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Step 1.5.2.1

Simplify each term.

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Step 1.5.2.1.1

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

$f (1) = 3 \cdot 0 - 2.75$

Step 1.5.2.1.2

Multiply $3$ by $0$ .

$f (1) = 0 - 2.75$

Step 1.5.2.2

Subtract $2.75$ from $0$ .

$f (1) = - 2.75$

Step 1.5.2.3

The final answer is $- 2.75$ .

$- 2.75$

Step 1.6

List the points in a table.

$\begin{array}{c} x & f (x) \\ - 1 & 6.675 \\ - \frac{1}{2} & 3.533 \\ 0 & 1.962 \\ \frac{1}{2} & 0.392 \\ 1 & - 2.75 \end{array}$

Step 2

The trig function can be graphed using the points.

$\begin{array}{c} x & f (x) \\ - 1 & 6.675 \\ - \frac{1}{2} & 3.533 \\ 0 & 1.962 \\ \frac{1}{2} & 0.392 \\ 1 & - 2.75 \end{array}$

Step 3