Trigonometry Examples

$y = 0.25 \arcsin (\frac{x}{2})$

Step 1

Select a few points to graph.

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Step 1.1

Find the point at $x = - 2$ .

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Step 1.1.1

Replace the variable $x$ with $- 2$ in the expression.

$f (- 2) = 0.25 \arcsin (\frac{- 2}{2})$

Step 1.1.2

Simplify the result.

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Step 1.1.2.1

Divide $- 2$ by $2$ .

$f (- 2) = 0.25 \arcsin (- 1)$

Step 1.1.2.2

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

$f (- 2) = 0.25 (- \frac{π}{2})$

Step 1.1.2.3

Cancel the common factor of $0.25$ .

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Step 1.1.2.3.1

Move the leading negative in $- \frac{π}{2}$ into the numerator.

$f (- 2) = 0.25 (\frac{- π}{2})$

Step 1.1.2.3.2

Factor $0.25$ out of $2$ .

$f (- 2) = 0.25 (\frac{- π}{0.25 (8)})$

Step 1.1.2.3.3

Cancel the common factor.

$f (- 2) = 0.25 (\frac{- π}{0.25 \cdot 8})$

Step 1.1.2.3.4

Rewrite the expression.

$f (- 2) = \frac{- π}{8}$

Step 1.1.2.4

Move the negative in front of the fraction.

$f (- 2) = - \frac{π}{8}$

Step 1.1.2.5

The final answer is $- \frac{π}{8}$ .

$- \frac{π}{8}$

Step 1.2

Find the point at $x = - 1$ .

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Step 1.2.1

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

$f (- 1) = 0.25 \arcsin (\frac{- 1}{2})$

Step 1.2.2

Simplify the result.

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Step 1.2.2.1

Move the negative in front of the fraction.

$f (- 1) = 0.25 \arcsin (- \frac{1}{2})$

Step 1.2.2.2

The exact value of $\arcsin (- \frac{1}{2})$ is $- \frac{π}{6}$ .

$f (- 1) = 0.25 (- \frac{π}{6})$

Step 1.2.2.3

Cancel the common factor of $0.25$ .

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Step 1.2.2.3.1

Move the leading negative in $- \frac{π}{6}$ into the numerator.

$f (- 1) = 0.25 (\frac{- π}{6})$

Step 1.2.2.3.2

Factor $0.25$ out of $6$ .

$f (- 1) = 0.25 (\frac{- π}{0.25 (24)})$

Step 1.2.2.3.3

Cancel the common factor.

$f (- 1) = 0.25 (\frac{- π}{0.25 \cdot 24})$

Step 1.2.2.3.4

Rewrite the expression.

$f (- 1) = \frac{- π}{24}$

Step 1.2.2.4

Move the negative in front of the fraction.

$f (- 1) = - \frac{π}{24}$

Step 1.2.2.5

The final answer is $- \frac{π}{24}$ .

$- \frac{π}{24}$

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.

$f (0) = 0.25 \arcsin (\frac{0}{2})$

Step 1.3.2

Simplify the result.

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Step 1.3.2.1

Divide $0$ by $2$ .

$f (0) = 0.25 \arcsin (0)$

Step 1.3.2.2

The exact value of $\arcsin (0)$ is $0$ .

$f (0) = 0.25 \cdot 0$

Step 1.3.2.3

Multiply $0.25$ by $0$ .

$f (0) = 0$

Step 1.3.2.4

The final answer is $0$ .

$0$

Step 1.4

Find the point at $x = 1$ .

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Step 1.4.1

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

$f (1) = 0.25 \arcsin (\frac{1}{2})$

Step 1.4.2

Simplify the result.

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Step 1.4.2.1

The exact value of $\arcsin (\frac{1}{2})$ is $\frac{π}{6}$ .

$f (1) = 0.25 (\frac{π}{6})$

Step 1.4.2.2

Cancel the common factor of $0.25$ .

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Step 1.4.2.2.1

Factor $0.25$ out of $6$ .

$f (1) = 0.25 (\frac{π}{0.25 (24)})$

Step 1.4.2.2.2

Cancel the common factor.

$f (1) = 0.25 (\frac{π}{0.25 \cdot 24})$

Step 1.4.2.2.3

Rewrite the expression.

$f (1) = \frac{π}{24}$

Step 1.4.2.3

The final answer is $\frac{π}{24}$ .

$\frac{π}{24}$

Step 1.5

Find the point at $x = 2$ .

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Step 1.5.1

Replace the variable $x$ with $2$ in the expression.

$f (2) = 0.25 \arcsin (\frac{2}{2})$

Step 1.5.2

Simplify the result.

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Step 1.5.2.1

Divide $2$ by $2$ .

$f (2) = 0.25 \arcsin (1)$

Step 1.5.2.2

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

$f (2) = 0.25 (\frac{π}{2})$

Step 1.5.2.3

Cancel the common factor of $0.25$ .

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Step 1.5.2.3.1

Factor $0.25$ out of $2$ .

$f (2) = 0.25 (\frac{π}{0.25 (8)})$

Step 1.5.2.3.2

Cancel the common factor.

$f (2) = 0.25 (\frac{π}{0.25 \cdot 8})$

Step 1.5.2.3.3

Rewrite the expression.

$f (2) = \frac{π}{8}$

Step 1.5.2.4

The final answer is $\frac{π}{8}$ .

$\frac{π}{8}$

Step 1.6

List the points in a table.

$\begin{array}{c} x & f (x) \\ - 2 & - \frac{π}{8} \\ - 1 & - \frac{π}{24} \\ 0 & 0 \\ 1 & \frac{π}{24} \\ 2 & \frac{π}{8} \end{array}$

Step 2

The trig function can be graphed using the points.

$\begin{array}{c} x & f (x) \\ - 2 & - \frac{π}{8} \\ - 1 & - \frac{π}{24} \\ 0 & 0 \\ 1 & \frac{π}{24} \\ 2 & \frac{π}{8} \end{array}$

Step 3