Trigonometry Examples

$x^{2} + {(y - \frac{5}{2})}^{2} = {(\frac{5}{2})}^{2}$

Step 1

Simplify ${(\frac{5}{2})}^{2}$ .

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Step 1.1

Apply the product rule to $\frac{5}{2}$ .

$x^{2} + {(y - \frac{5}{2})}^{2} = \frac{5^{2}}{2^{2}}$

Step 1.2

Raise $5$ to the power of $2$ .

$x^{2} + {(y - \frac{5}{2})}^{2} = \frac{25}{2^{2}}$

Step 1.3

Raise $2$ to the power of $2$ .

$x^{2} + {(y - \frac{5}{2})}^{2} = \frac{25}{4}$

Step 2

This is the form of a circle. Use this form to determine the center and radius of the circle.

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$

Step 3

Match the values in this circle to those of the standard form. The variable $r$ represents the radius of the circle, $h$ represents the x-offset from the origin, and $k$ represents the y-offset from origin.

$r = \frac{5}{2}$

$h = 0$

$k = \frac{5}{2}$

Step 4

The center of the circle is found at $(h, k)$ .

Center: $(0, \frac{5}{2})$

Step 5

These values represent the important values for graphing and analyzing a circle.

Center: $(0, \frac{5}{2})$

Radius: $\frac{5}{2}$

Step 6