Trigonometry Examples

$\arcsin (x) - 90$

Step 1

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.

$f (- 1) = \arcsin (- 1) - 90$

Simplify the result.

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

$f (- 1) = - \frac{π}{2} - 90$

The final answer is $- \frac{π}{2} - 90$ .

$- \frac{π}{2} - 90$

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

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

$f (- \frac{1}{2}) = \arcsin (- \frac{1}{2}) - 90$

Simplify the result.

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

$f (- \frac{1}{2}) = - \frac{π}{6} - 90$

The final answer is $- \frac{π}{6} - 90$ .

$- \frac{π}{6} - 90$

Find the point at $x = 0$ .

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

$f (0) = \arcsin (0) - 90$

Simplify the result.

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

$f (0) = 0 - 90$

Subtract $90$ from $0$ .

$f (0) = - 90$

The final answer is $- 90$ .

$- 90$

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

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

$f (\frac{1}{2}) = \arcsin (\frac{1}{2}) - 90$

Simplify the result.

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

$f (\frac{1}{2}) = \frac{π}{6} - 90$

The final answer is $\frac{π}{6} - 90$ .

$\frac{π}{6} - 90$

Find the point at $x = 1$ .

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

$f (1) = \arcsin (1) - 90$

Simplify the result.

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

$f (1) = \frac{π}{2} - 90$

The final answer is $\frac{π}{2} - 90$ .

$\frac{π}{2} - 90$

List the points in a table.

$\begin{array}{c} x & f (x) \\ - 1 & - \frac{π}{2} - 90 \\ - \frac{1}{2} & - \frac{π}{6} - 90 \\ 0 & - 90 \\ \frac{1}{2} & \frac{π}{6} - 90 \\ 1 & \frac{π}{2} - 90 \end{array}$

Step 2

The trig function can be graphed using the points.

$\begin{array}{c} x & f (x) \\ - 1 & - \frac{π}{2} - 90 \\ - \frac{1}{2} & - \frac{π}{6} - 90 \\ 0 & - 90 \\ \frac{1}{2} & \frac{π}{6} - 90 \\ 1 & \frac{π}{2} - 90 \end{array}$

Step 3