Sample with MathJax content

The toolbar will appear after this button is clicked

Start reading here. $\frac{1}{3}$

Delta Symbol: $Δ y = y_{2} - y_{1}$

Included in a sentence here $\frac{1}{5}$ .

Given the quadratic equation $a x^{2} + b x + c = 0$ , one of the two roots is given by $x = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$

$\sqrt{49}$

You should be able to see this inline equation: $x^{2} + {x y}^{2} + {x y z}^{2} = 0$

The area of a circle is : $π r^{2}$

$x^{2} + x^{3} + x^{4} + x^{5}$

Accelerate

You have learned that the ratio of the circumference of a circle to its diameter is equal to $π$ or approximately 3.14. This relationship is shown in the equation:

$π = \frac{c}{d}$

$c = π \times d$

The circumference of any circle is $2 π r$ or approximately 6.28 times the length of the radius.

Angles are commonly drawn as arcs. A 45° angle is shown on the unit circle in standard position on this graph. In this image, the arc is shown in green. In geometry, to subtend means to take up the side opposite a given angle. We would say that the arc shown in green subtends a 45° angle.

The length of an arc is the distance between the two endpoints of the arc. The arc depicted in this image has a length equal to $\frac{1}{8}$ of the circumference of the circle (because 45° is $\frac{1}{8}$ of a circle, 360°). Since the circumference of a unit circle is 2 $π$ , the length of this arc is $\frac{1}{8}$ of that value, or $\frac{π}{4}$ .

$x = c \frac{n}{360}$

The radian measure that corresponds to a degree measure can be found by calculating the arc that angle intercepts on the unit circle. The equation for this is $x rad = 2 π \frac{n^{\circ}}{360^{\circ}}$ . Use this equation to match the radian measures below with their corresponding degree measures.

Every 30° is equal to $\frac{π}{6}$ rad.

Therefore:

30° is equal to $\frac{π}{6}$ rad.

60° is equal to $\frac{2 π}{6}$ , or $\frac{π}{3}$ rad.

90° is equal to $\frac{3 π}{6}$ , or $\frac{π}{2}$ rad, and so on.

Many problems in physics and engineering require the angle measurements to be delivered in radians. Fortunately, converting from degrees to radians is not difficult. In the video below, an instructor will demonstrate how to convert between degrees and radians by multiplying by a conversion factor (either $\frac{180^{\circ}}{π rad}$ or $\frac{π rad}{180^{\circ}}$ ).

Web reference

MathML specification

Sample with MathJax content

Accelerate

Every 30° is equal to &#x03C0; 6 rad.

Every 30° is equal to $\frac{π}{6}$ rad.