Graph y=arcsin(x)+pi/2

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Trigonometry

$y = \arcsin (x) + \frac{π}{2}$

Select a few points to graph.

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Find the point at $x = - 1$ .

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

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

Simplify the result.

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

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

Combine the numerators over the common denominator.

$f (- 1) = \frac{- π + π}{2}$

Add $- π$ and $π$ .

$f (- 1) = \frac{0}{2}$

Divide $0$ by $2$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

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

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

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

Simplify the result.

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

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

To write $\frac{π}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{π}{2}$ and $\frac{3}{3}$ .

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

Multiply $2$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Move $3$ to the left of $π$ .

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

Add $- π$ and $3 π$ .

$f (- \frac{1}{2}) = \frac{2 π}{6}$

Cancel the common factor of $2$ and $6$ .

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Factor $2$ out of $2 π$ .

$f (- \frac{1}{2}) = \frac{2 (π)}{6}$

Cancel the common factors.

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Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$f (- \frac{1}{2}) = \frac{π}{3}$

The final answer is $\frac{π}{3}$ .

$\frac{π}{3}$

Find the point at $x = 0$ .

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

$f (0) = \arcsin (0) + \frac{π}{2}$

Simplify the result.

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

$f (0) = 0 + \frac{π}{2}$

Add $0$ and $\frac{π}{2}$ .

$f (0) = \frac{π}{2}$

The final answer is $\frac{π}{2}$ .

$\frac{π}{2}$

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

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

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

Simplify the result.

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

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

To write $\frac{π}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$f (\frac{1}{2}) = \frac{π}{6} + \frac{π}{2} \cdot \frac{3}{3}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{π}{2}$ and $\frac{3}{3}$ .

$f (\frac{1}{2}) = \frac{π}{6} + \frac{π \cdot 3}{2 \cdot 3}$

Multiply $2$ by $3$ .

$f (\frac{1}{2}) = \frac{π}{6} + \frac{π \cdot 3}{6}$

Combine the numerators over the common denominator.

$f (\frac{1}{2}) = \frac{π + π \cdot 3}{6}$

Simplify the numerator.

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Move $3$ to the left of $π$ .

$f (\frac{1}{2}) = \frac{π + 3 \cdot π}{6}$

Add $π$ and $3 π$ .

$f (\frac{1}{2}) = \frac{4 π}{6}$

Cancel the common factor of $4$ and $6$ .

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Factor $2$ out of $4 π$ .

$f (\frac{1}{2}) = \frac{2 (2 π)}{6}$

Cancel the common factors.

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Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$f (\frac{1}{2}) = \frac{2 π}{3}$

The final answer is $\frac{2 π}{3}$ .

$\frac{2 π}{3}$

Find the point at $x = 1$ .

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

$f (1) = \arcsin (1) + \frac{π}{2}$

Simplify the result.

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

$f (1) = \frac{π}{2} + \frac{π}{2}$

Combine the numerators over the common denominator.

$f (1) = \frac{π + π}{2}$

Add $π$ and $π$ .

$f (1) = \frac{2 π}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$f (1) = \frac{2 π}{2}$

Divide $π$ by $1$ .

$f (1) = π$

The final answer is $π$ .

$π$

List the points in a table.

$\begin{array}{c} x & f (x) \\ - 1 & 0 \\ - \frac{1}{2} & \frac{π}{3} \\ 0 & \frac{π}{2} \\ \frac{1}{2} & \frac{2 π}{3} \\ 1 & π \end{array}$

The trig function can be graphed using the points.

$\begin{array}{c} x & f (x) \\ - 1 & 0 \\ - \frac{1}{2} & \frac{π}{3} \\ 0 & \frac{π}{2} \\ \frac{1}{2} & \frac{2 π}{3} \\ 1 & π \end{array}$

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