Table of Contents
Quadrant (I)
Quadrant- Infinity Learn: The first quadrant is a region of the coordinate plane consisting of the points (x, y) that satisfy the equation x ≥ 0. This means that all points in the first quadrant have positive x-coordinates. Points in the first quadrant are located in the upper-left corner of the coordinate plane.
A quadrant is a mathematical tool that is used to measure angles. It is made up of a straight edge and a compass. The compass is used to draw circles and the straight edge is used to measure the length of the line segments that are created.
Second Quadrant (II)
In the second quadrant, the x-axis represents the independent variable and the y-axis represents the dependent variable. The equation in this quadrant is y = mx + b, where m is the slope and b is the y-intercept.
In this quadrant, the slope is positive, meaning that the line slopes upward from left to right. The y-intercept is also positive, meaning that the line intersects the y-axis at a positive point. This quadrant represents a situation in which the independent variable increases as the dependent variable increases.
Third Quadrant (III)
In the third quadrant, the y-axis is the independent variable and the x-axis is the dependent variable. The graph will be a parabola that opens down.
The equation of the parabola will be y = ax2.
In this quadrant, the slope of the line will be negative.
Fourth Quadrant (IV)
The fourth quadrant is the realm of the unknown and the unexpected. It is the place where new ideas and new possibilities can be born. It is also the place where chaos and confusion can reign.
In order to make the most of the fourth quadrant, it is important to be open to new possibilities and to be prepared for anything. It is also important to be able to handle chaos and confusion, and to stay focused on your goals.
Trigonometric Values in a Different Quadrant
A trigonometric value in a different quadrant can be found by using the inverse of the trigonometric function. The inverse function will take the angle and the quadrant number and return the value in that quadrant.
For example, if you need the value of cosine in the third quadrant, you would use the inverse function, cos-1, and input the angle in radians. The value that is returned will be the cosine value in the third quadrant.
A right triangle has three sides: the hypotenuse, the opposite side, and the adjacent side. The hypotenuse is the longest side of the triangle and the other two sides are the short sides. The opposite side is the side that is opposite of the angle that is being measured. The adjacent side is the side that is next to the angle that is being measured. The angles of a right triangle are measured in radians.
There are six trigonometric values in a right triangle: the sine, the cosine, the tangent, the cosecant, the secant, and the cotangent. The sine, the cosine, and the tangent are all measures of angles in radians. The cosecant, the secant, and the cotangent are all measures of angles in radians squared.
The sine of an angle is the length of the opposite side divided by the length of the hypotenuse. The cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse. The tangent of an angle is the length of the opposite side divided by the length of the adjacent side.
The cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side. The secant of an angle is the length of the hypotenuse divided by the length of the adjacent side. The cotangent of an angle is the length of the adjacent side divided by the length of the opposite side.
