Trigonometry Examples

$y = \frac{1}{2} \cdot \arcsin (x)$

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 $x$ .

$0 = \frac{1}{2} \cdot \arcsin (x)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{1}{2} \cdot \arcsin (x) = 0$ .

$\frac{1}{2} \cdot \arcsin (x) = 0$

Step 1.2.2

Multiply each term in $\frac{1}{2} \cdot \arcsin (x) = 0$ by $2$ to eliminate the fractions.

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Step 1.2.2.1

Multiply each term in $\frac{1}{2} \cdot \arcsin (x) = 0$ by $2$ .

$\frac{1}{2} \cdot \arcsin (x) \cdot 2 = 0 \cdot 2$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Combine $\frac{1}{2}$ and $\arcsin (x)$ .

$\frac{\arcsin (x)}{2} \cdot 2 = 0 \cdot 2$

Step 1.2.2.2.2

Cancel the common factor of $2$ .

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Step 1.2.2.2.2.1

Cancel the common factor.

$\frac{\arcsin (x)}{2} \cdot 2 = 0 \cdot 2$

Step 1.2.2.2.2.2

Rewrite the expression.

$\arcsin (x) = 0 \cdot 2$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Multiply $0$ by $2$ .

$\arcsin (x) = 0$

Step 1.2.3

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

$x = \sin (0)$

Step 1.2.4

Simplify the right side.

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Step 1.2.4.1

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

$x = 0$

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

$y = \frac{1}{2} \cdot \arcsin (0)$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{1}{2} \cdot \arcsin (0)$

Step 2.2.2

Simplify $\frac{1}{2} \cdot \arcsin (0)$ .

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Step 2.2.2.1

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

$y = \frac{1}{2} \cdot 0$

Step 2.2.2.2

Multiply $\frac{1}{2}$ by $0$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

Step 3

List the intersections.

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

y-intercept(s): $(0, 0)$

Step 4