Structural information from multiple conformational states is represented by a graph whose nodes correspond to amino acids. We develop a graph-based method for detecting rigid domains in proteins. Despite previous efforts, there is a need to develop new domain segmentation algorithms that are capable of analysing the entire structure database efficiently and do not require the choice of protein-dependent tuning parameters such as the number of rigid domains. Structural changes in proteins can be described approximately as the relative movement of rigid domains against each other.
Once we've memorized the values, or if we have a reference of some sort, it becomes relatively simple to recognize and determine sine or arcsine values for the special angles.Conformational transitions are implicated in the biological function of many proteins. This pattern repeats periodically for the respective angle measurements, and we can identify the values of sin(θ) based on the position of θ in the unit circle, taking the sign of sine into consideration: sine is positive in quadrants I and II and negative in quadrants III and IV. The values of sine from 0° through -90° follows the same pattern except that the values are negative instead of positive since sine is negative in quadrant IV. The subsequent values, sin(30°), sin(45°), sin(60°), and sin(90°) follow a pattern such that using the value of sin(0°) as a reference, to find the values of sine for the subsequent angles, we simply increase the number under the radical sign in the numerator by 1, as shown below. Starting from 0° progressing through 90°, sin(0°) = 0 =. One method that may help with memorizing these values is to express all the values of sin(θ) as fractions involving a square root.
Below is a table showing these angles (θ) in both radians and degrees, and their respective sine values, sin(θ). While we can find the value of arcsine 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 sine and arcsine values may be worth memorizing. The following is a calculator to find out either the arccos value of a number between -1 and 1 or cosine value of an angle. The domain of arcsin(x), -1≤x≤1, is the range of sin(x), and its range, ≤y≤, is the domain of sin(x). The graph of y = arcsin(x) is shown below.Īs can be seen from the figure, y = arcsin(x) is a reflection of sin(x), given the restricted domain ≤x≤, across the line y = x. 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. Since sine is a periodic function, without restricting the domain, a horizontal line would intersect the function periodically, infinitely many times.
The domain must be restricted because in order for a function to have an inverse, the function must be one-to-one, meaning that no horizontal line can intersect the graph of the function more than once.
In the figure below, the portion of the graph highlighted in red shows the portion of the graph of sin(x) that has an inverse. Sine only has an inverse on a restricted domain, ≤x≤. Home / trigonometry / trigonometric functions / arcsin ArcsinĪrcsine, written as arcsin or sin -1 (not to be confused with ), is the inverse sine function.
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