Trigonometry Examples

$y = \arccos (x)$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \arccos (x)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\arccos (x) = 0$ .

$\arccos (x) = 0$

Step 1.2.2

Take the inverse arccosine of both sides of the equation to extract $x$ from inside the arccosine.

$x = \cos (0)$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

The exact value of $\cos (0)$ is $1$ .

$x = 1$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(1, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \arccos (0)$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \arccos (0)$

Step 2.2.2

The exact value of $\arccos (0)$ is $\frac{π}{2}$ .

$y = \frac{π}{2}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{π}{2})$

Step 3

List the intersections.

x-intercept(s): $(1, 0)$

y-intercept(s): $(0, \frac{π}{2})$

Step 4