csc(x)
The term “csc(x)” stands for the cosecant function of x, where x is an angle measured in radians
The term “csc(x)” stands for the cosecant function of x, where x is an angle measured in radians. Cosecant is one of the six trigonometric functions and is defined as the ratio of the hypotenuse to the length of the side opposite to a given angle in a right triangle.
To understand the cosecant function, it is helpful to examine a unit circle. A unit circle has a radius of 1 and is centered at the origin of a coordinate plane. The angle x is formed by the terminal side of a ray (starting from the origin) and the positive x-axis.
In a unit circle, the cosecant (csc) of an angle is defined as the reciprocal of the sine (sin) of that angle. Mathematically, it can be expressed as:
csc(x) = 1 / sin(x)
Here’s how you can interpret the csc(x) function in different quadrants:
– In the first quadrant (0° to 90° or 0 to π/2 radians), both the sine and cosecant functions are positive.
– In the second quadrant (90° to 180° or π/2 to π radians), the sine function becomes positive, but the cosecant function is negative.
– In the third quadrant (180° to 270° or π to 3π/2 radians), both the sine and cosecant functions are negative.
– In the fourth quadrant (270° to 360° or 3π/2 to 2π radians), the sine function becomes positive, but the cosecant function is negative.
The values of the cosecant function can be found using trigonometric tables or calculators. For example, if you need to find csc(30°), you would evaluate the reciprocal of sin(30°), which is approximately 2.
It’s important to note that the cosecant function is undefined when the sine function equals zero. This occurs at 0°, 180°, 360°, and any other angle formed by multiples of 180°.
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