3/22/2023 0 Comments Unit circle tangent![]() There are other ways of measuring angles, one, and this is also found on nearly all scientific calculators, are radians. The way that you are probably familiar with is using degrees. If you wanted to describe it then you could say that it is the distance of the point of intersection of the angle line and the line perpendicular to the x-axis from the x-axis, which is of distance 1 from the origin!Īnother thing that you may have noticed on calculators is that you can measure angles in different ways. It is actually easier to see on a diagram than it is to say by words. The tangent function and the unit circleĭoes the unit circle provide an easy way of getting tangents, in the same way, that it does for sine and cosine? The answer is yes. ![]() We will try to answer this in the next paragraph. Is tangent easily seen on the unit circle? As you are probably well aware, this function is also on scientific calculators. There is another function that is important in trigonometry and this is the tangent function. With calculators, it is easy to get the trigonometric functions of angles greater than 90 o or less than 0 o. This is a skill that you probably have already, so we won’t dwell on it in this article. CalculatorsĪn examination of any scientific calculator will show that sines and cosines can be worked out very easily using these devices. It is impossible to meaningfully get the trigonometric functions in such situations of angles greater than 90 o or less than 0 o. We mentioned before that in early math courses, where trigonometry is introduced in high school, students are taught about Pythagoras’ Theorem and using the trigonometric functions to find sides and angles of right-angled triangles in both theoretical and practical situations. Early Trigonometry: Pythagoras and SOHCAHTOA We can have negative angles, but they go clockwise. Note that the angles are positive and go anti-clockwise. The diagrams below show how this can be done. ![]() This is really useful because using this method of defining the sine and cosine functions, we can easily find the sine and cosine of such angles as 120 o, 223 o, and 310 o, which was impossible with the right-angled triangles of early math courses, where trigonometry is introduced, in high school. The unit circle gives an easy method of defining the sine and cosine functions that you have probably met before, since for an arbitrary angle (see diagram below), the radius making an angle with the x-axis cuts the unit circle at the point whose x-coordinate is cos and whose y-coordinate is sin. The unit circle is a circle in the Cartesian plane centred at (0,0), often called the origin, with radius 1. C is centred at (1,-2) and has a radius of 2. B is centred at (0,0) and has a radius of 2. A is centred at (0,0) and has a radius of 3. The diagram above shows 3 circles in a coordinate or Cartesian plane. Shorter, straight lines, which don’t go through the centre, connecting different parts of the circle are called arcs. The longer line is twice the radius and is called the diameter. No matter what point you choose on the circle, the shortest distance to the centre is the radius, which always has the same length. The length of a circle is called its circumference. Before we start though, we should ask, what is a circle? What is a circle?Ī circle is a very important shape (a shape is sometimes called a locus) that consists of all points in a plane, which are at a given distance called the radius from a particular point called the centre. This short article on a type of circle is quite straightforward but it has very important applications to the mathematical field of trigonometry.
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