For Texas Instruments calculators, press the button, then use the arrow keys to highlight DEGREE, and press. If you are dealing with degrees, it is important to make sure that your calculator is in “degrees” mode first. However, they can only process in terms of one or the other at a single time. Scientific calculators are programmed to perform many different functions, including working with both degrees and radians. Using the correct mode in your calculator. Usually, we don’t need to use polar coordinates until we get into content from Calculus II, but it can be helpful to see that this is one application for which we use radians in mathematics. The lowercase r is a parameter specifying how far away the point is from the origin, and the Greek letter (pronounced “they-ta”) specifies at which angle the point is from the positive x-axis. What are polar coordinates? In the same way that we usually use ordered pairs \((x,y)\) to describe points on the Cartesian plane, we can also describe points using the polar coordinates \((r,θ)\). Remember that there are 360° in a circle, and that there are \(2\pi\) radians in a circle. How do we convert from degrees to radians? We need a way to convert our number of degrees into some number of radians, so we will derive a conversion factor with which to do so. We most commonly use radians when dealing with the trigonometric functions (sin, cos, tan, csc, sec, and cot). Rad to deg full#
In other words, one full revolution contains \(2\pi\) radians. And since the length of the circle’s radius is equal to one radian, the circumference is equal to \(2\pi\) radians. The circumference of a circle is equal to \(\pi\) times its diameter, or equivalently, times twice its radius. So how many radians are in a full revolution then? Recall the relationship between the radius of a circle and its circumference.
Notice from the illustration above that the angle of one radian is almost one sixth of the circle. One radian is the angle at which the radius of the circle equals the length of the arc of the curve drawn with that angle. Rather than divide a circle into 360 tiny “slices”, radians offer a clever and intuitive way to measure angles. What are radians, and how do we use them? Radians are simply another way of measuring angles.
For this reason, the positive x -axis is referred to as 0° in polar coordinates, which we will address later.
Note that when we use angles on the Cartesian plane, the angles always begin on the positive x -axis and open in the counterclockwise direction.
A full circle contains 360°, and a 360° angle is called a complete angle. The small circle symbol “ ° ” (pronounced “degrees”) is used following a number to denote that degrees are being represented. What are degrees, and how do we use them? We use degrees as units of measurement for angles, and precisely determining how wide or narrow they are.
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