Graph y=arcsin(x-1)

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Trigonometry

Graph y=arcsin(x-1)

$y = \arcsin (x - 1)$

Select a few points to graph.

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Find the point at $x = 0$ .

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

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

Simplify the result.

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Subtract $1$ from $0$ .

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

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

$f (0) = - \frac{π}{2}$

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.

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

Simplify the result.

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To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $- 1$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Multiply $- 1$ by $2$ .

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

Subtract $2$ from $1$ .

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

Move the negative in front of the fraction.

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

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

$f (\frac{1}{2}) = - \frac{π}{6}$

The final answer is $- \frac{π}{6}$ .

$- \frac{π}{6}$

Find the point at $x = 1$ .

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

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

Simplify the result.

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Subtract $1$ from $1$ .

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

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

$f (1) = 0$

The final answer is $0$ .

$0$

Find the point at $x = \frac{3}{2}$ .

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Replace the variable $x$ with $\frac{3}{2}$ in the expression.

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

Simplify the result.

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To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $- 1$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Multiply $- 1$ by $2$ .

$f (\frac{3}{2}) = \arcsin (\frac{3 - 2}{2})$

Subtract $2$ from $3$ .

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

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

$f (\frac{3}{2}) = \frac{π}{6}$

The final answer is $\frac{π}{6}$ .

$\frac{π}{6}$

Find the point at $x = 2$ .

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

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

Simplify the result.

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Subtract $1$ from $2$ .

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

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

$f (2) = \frac{π}{2}$

The final answer is $\frac{π}{2}$ .

$\frac{π}{2}$

List the points in a table.

$\begin{array}{c} x & f (x) \\ 0 & - \frac{π}{2} \\ \frac{1}{2} & - \frac{π}{6} \\ 1 & 0 \\ \frac{3}{2} & \frac{π}{6} \\ 2 & \frac{π}{2} \end{array}$

The trig function can be graphed using the points.

$\begin{array}{c} x & f (x) \\ 0 & - \frac{π}{2} \\ \frac{1}{2} & - \frac{π}{6} \\ 1 & 0 \\ \frac{3}{2} & \frac{π}{6} \\ 2 & \frac{π}{2} \end{array}$

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Name

Name	one billion ninety-nine million one hundred eighty-nine thousand eighty-five

Interesting facts

1099189085 has 4 divisors, whose sum is 1319026908
The reverse of 1099189085 is 5809819901
Previous prime number is 5

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 50
Digital Root 5

Name

Name	one billion nine hundred seventy-four million two hundred eighty-six thousand eight hundred seventy-three

Interesting facts

1974286873 has 8 divisors, whose sum is 2135524608
The reverse of 1974286873 is 3786824791
Previous prime number is 227

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 55
Digital Root 1

Name

Name	six hundred forty-seven million five hundred eighteen thousand three hundred fifty-five

Interesting facts

647518355 has 32 divisors, whose sum is 912316608
The reverse of 647518355 is 553815746
Previous prime number is 17

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 44
Digital Root 8

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