Cosecant Math

For example the triangle contains an angle a and the ratio of the side opposite to a and the side opposite to the right angle the hypotenuse is.

Cosecant math. F x csc x is a periodic function with period 2π. Sec cosec and cot a level maths revision. The abbreviation is csc csc θ hypotenuse opposite it is not commonly used and is equal to 1 sine. Cosecant abbreviated as csc is the reciprocal of the sine function the cosecant function.

Sine cosine and tangent often shortened to sin cos and tan are each a ratio of sides of a right angled triangle. To unlock this lesson. The inverse cosecant function arccsc. The circle definition a generalization of sohcahtoa is shown below on the right.

Other articles where cosecant is discussed. In a right angled triangle the cosecant of an angle is. Secant cosecant and cotangent are usually written as sec cosec and cot they are trigonometric functions. In mathematics the trigonometric functions also called circular functions angle functions or goniometric functions are real functions which relate an angle of a right angled triangle to ratios of two side lengths.

For every trigonometry function such as csc there is an inverse function that works in reverse. These inverse functions have the same name but with arc in front. So the inverse of csc is arccsc etc. Sine cosine and tangent.

In a right triangle with an angle theta csc theta frac text hypotenuse text opposite text opposite is the side of the triangle not part of angle theta and text hypotenuse is the side opposite the right angle. The length of the hypotenuse divided by the length of the side opposite the angle. They are widely used in all sciences that are related to geometry such as navigation solid mechanics celestial mechanics geodesy and many others. Using the unit circle ordered pairs we just take the y term and flip it over.

These six trigonometric functions in relation to a right triangle are displayed in the figure. Cosecant csc is a trigonometric ratio. Cotangent cot secant sec and cosecant csc. Properties the reciprocal of cosecant is sine abbreviated as sin while its.

Divide the length of one side by another side. It is generally written in ratio form and also written as cosecant with angle in alternate way. For a given angle θ each ratio stays the same no matter how big or small the triangle is. Cosecant is a name and it is introduced in trigonometry mathematics to denote the ratio of lengths of hypotenuse to opposite side at a particular angle in a right triangle.