Trigonometry Examples

$y = 1 - \arcsin (x)$

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.

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

Step 1.1.2

Simplify the result.

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Step 1.1.2.1

Simplify each term.

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Step 1.1.2.1.1

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

$f (- 1) = 1 + \frac{π}{2}$

Step 1.1.2.1.2

Multiply $- - \frac{π}{2}$ .

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Step 1.1.2.1.2.1

Multiply $- 1$ by $- 1$ .

$f (- 1) = 1 + 1 (\frac{π}{2})$

Step 1.1.2.1.2.2

Multiply $\frac{π}{2}$ by $1$ .

$f (- 1) = 1 + \frac{π}{2}$

Step 1.1.2.2

The final answer is $1 + \frac{π}{2}$ .

$1 + \frac{π}{2}$

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.

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

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 $\arcsin (- \frac{1}{2})$ is $- \frac{π}{6}$ .

$f (- \frac{1}{2}) = 1 + \frac{π}{6}$

Step 1.2.2.1.2

Multiply $- - \frac{π}{6}$ .

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Step 1.2.2.1.2.1

Multiply $- 1$ by $- 1$ .

$f (- \frac{1}{2}) = 1 + 1 (\frac{π}{6})$

Step 1.2.2.1.2.2

Multiply $\frac{π}{6}$ by $1$ .

$f (- \frac{1}{2}) = 1 + \frac{π}{6}$

Step 1.2.2.2

The final answer is $1 + \frac{π}{6}$ .

$1 + \frac{π}{6}$

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.

$f (0) = 1 - \arcsin (0)$

Step 1.3.2

Simplify the result.

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Step 1.3.2.1

Simplify each term.

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Step 1.3.2.1.1

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

$f (0) = 1 - 0$

Step 1.3.2.1.2

Multiply $- 1$ by $0$ .

$f (0) = 1 + 0$

Step 1.3.2.2

Add $1$ and $0$ .

$f (0) = 1$

Step 1.3.2.3

The final answer is $1$ .

$1$

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.

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

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 $\frac{π}{6}$ .

$f (\frac{1}{2}) = 1 - \frac{π}{6}$

Step 1.4.2.2

The final answer is $1 - \frac{π}{6}$ .

$1 - \frac{π}{6}$

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.

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

Step 1.5.2

Simplify the result.

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Step 1.5.2.1

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

$f (1) = 1 - \frac{π}{2}$

Step 1.5.2.2

The final answer is $1 - \frac{π}{2}$ .

$1 - \frac{π}{2}$

Step 1.6

List the points in a table.

$\begin{array}{c} x & f (x) \\ - 1 & 1 + \frac{π}{2} \\ - \frac{1}{2} & 1 + \frac{π}{6} \\ 0 & 1 \\ \frac{1}{2} & 1 - \frac{π}{6} \\ 1 & 1 - \frac{π}{2} \end{array}$

Step 2

The trig function can be graphed using the points.

$\begin{array}{c} x & f (x) \\ - 1 & 1 + \frac{π}{2} \\ - \frac{1}{2} & 1 + \frac{π}{6} \\ 0 & 1 \\ \frac{1}{2} & 1 - \frac{π}{6} \\ 1 & 1 - \frac{π}{2} \end{array}$

Step 3