Properties, or actually operate on functions to make new functions. We can compare different functions, discuss their Process of evaluating a particular expression, so we can talk about When you use this equation with every possible x-value and y-value and graph the points you are able to make, you will construct a circle.īasically, the concept of functions gives us a way to name the whole For example, another point on our circle is (3/√2, 3/√2). You will find that this works for every single point on the circle. Using this in the Pythagorean theorem, we find:ĭoes this work for the point we selected (aka (3, 0))? The hypotenuse would be the radius of our circle. The base of the triangle would be the x-axis, and the adjacent side would be some y-value. Since this is a right triangle, we should be able to apply the Pythagorean theorem. Let's try to make a right triangle, where the center of the circle is one vertex, and its opposite vertex is the outer edge. Let's find some points on the outer edge of the circle.Ī noticeable one is (3, 0) (3 units away from the center). Once we've memorized the values, or if we have a reference of some sort, it becomes relatively simple to recognize and determine tangent or arctangent values for the special angles.Let's consider a circle with center (0, 0) (to make the explanation a little simpler) and radius 3. Refer to their respective pages to view a method that may help with memorizing sine and cosine values. , and determine the value for tan(θ) based on the sine and cosine values, which follow a pattern that may be easier to memorize. To find tan(θ), we either need to just memorize the values, or remember that tan(θ)= Below is a table showing these angles (θ) in both radians and degrees, and their respective tangent values, tan(θ). While we can find the value for arctangent for any x value in the interval, there are certain angles that are used frequently in trigonometry (0°, 30°, 45°, 60°, 90°, and their multiples and radian equivalents) whose tangent and arctangent values may be worth memorizing. The following is a calculator to find out either the arctan value of a number or tangent value of an angle. Since tangent is a periodic function, without restricting the domain, a horizontal line would intersect the function periodically, infinitely many times. The reason that the domain of y = tan(x) must be restricted is because in order for a function to have an inverse, the function must be one-to-one, which means that no horizontal line can intersect the graph of the function more than once. Notice that tangent only has an inverse function on a restricted domain,, highlighted in red, and that this restricted domain is the range of y = arctan(x). We can see this if we look at the graph y = tan(x), shown below: This effectively means that the graph of the inverse function is a reflection of the graph of the function across the line y = x. One of the properties of inverse functions is that if a point (a, b) is on the graph of f, the point (b, a) is on the graph of its inverse. The domain of y = arctan(x) is all x values and its range is. The graph of y = arctan(x) is shown below. Home / trigonometry / trigonometric functions / arctan ArctanĪrctangent, written as arctan or tan -1 (not to be confused with ) is the inverse tangent function.
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