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Why is cotangent positive in the third quad?
If you are familiar with trigonometric functions defined in terms of the unit circle, the x and y coordinates are negative in the third quadrant. As a result, x/y, the ratio that defines cotangent, is positive.
What are the quadrant angles?
Quadrant angles are angles formed in the coordinate plane by the x-axis and y-axis. Each quadrant is a region bounded by the x-axis and y-axis, and is numbered counterclockwise starting from the positive x-axis. The angles in each quadrant have specific characteristics based on their trigonometric ratios, such as sine, cosine, and tangent values. In trigonometry, understanding quadrant angles is crucial for determining the sign of trigonometric functions and solving equations involving angles.
What are the quadrants in math?
There are four quadrants. They are represented by Roman numerals : I(one), II(two), III(three), IV(four). The first quadrant contains all positive points , (+x, +y) The second quadrant contains negative x's and positive y's , (-x, +y) The third quadrant is all negative , (-x, -y) The fourth quadrant has negative y's and positive x's , (+x, -y)
What quadrant does -135 degrees?
Third quadrant. From the origin (0,0) and on the positive x-axis. Move an arrow/line clockwise from this axis by 135 degrees. The first 90 degrees are in the bottom right (4th)quandrant. The next 90 degrees(to 180 degrees ; includes 135) will be in the bottom left (3rd) quadrant. NB From the positive x-axis ,moving anti-clockwise about the origin the angles are positive. When moving clockwise from the same axis the angles are negative.
What are the trigonometric functions and ratios?
In all there are [at least] 24 trigonometric functions and ratios. Half of these are circular and the other half are hyperbolic. Sine and Cosine are basic trigonometric funtions, abbreviated as sin and cos. Tangent is the third basic ratio defined as Sin/Cos. For each of these three, there is a corresponding reciprocal function: Sine -> Cosecant (cosec or csc) Cosine -> Secant (sec) Tangent -> Cotangent (cot). Each of the above six has an inverse function, defined on an appropriate domain. They all are named by adding the prefix "arc", for example arcsin, which is usually written as sin-1. The above are the circular functions. Each one of them has a corresponding hyperbolic equivalent. These are named by adding the suffix, "h", thus cosh, sech, arccosh [= cosh-1], etc.
