trigonometric

(adjective)

relating to the functions used in trigonometry: $\sin$, $\cos$, $\tan$, $\csc$, $\cot$, $\sec$

Related Terms

Examples of trigonometric in the following topics:

  • Inverse Trigonometric Functions: Differentiation and Integration

    • It is useful to know the derivatives and antiderivatives of the inverse trigonometric functions.
    • The inverse trigonometric functions are also known as the "arc functions".
    • There are three common notations for inverse trigonometric functions.
    • They can be thought of as the inverses of the corresponding trigonometric functions.
    • The differentiation of trigonometric functions is the mathematical process of finding the rate at which a trigonometric function changes with respect to a variable.

  • Finding Angles From Ratios: Inverse Trigonometric Functions

    • The inverse trigonometric functions can be used to find the acute angle measurement of a right triangle.
    • Using the trigonometric functions to solve for a missing side when given an acute angle is as simple as identifying the sides in relation to the acute angle, choosing the correct function, setting up the equation and solving.  
    • In order to solve for the missing acute angle, use the same three trigonometric functions, but, use the inverse key ($^{-1}$on the calculator) to solve for the angle ($A$) when given two sides.
    • Therefore, use the sine trigonometric function.
    • Recognize the role of inverse trigonometric functions in solving problems about right triangles

  • Derivatives of Trigonometric Functions

    • Derivatives of trigonometric functions can be found using the standard derivative formula.
    • The trigonometric functions (also called the circular functions) are functions of an angle.
    • Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.
    • The most familiar trigonometric functions are the sine, cosine, and tangent.
    • The same procedure can be applied to find other derivatives of trigonometric functions.

  • How Trigonometric Functions Work

    • Trigonometric functions can be used to solve for missing side lengths in right triangles.
    • We can define the trigonometric functions in terms an angle $t$ and the lengths of the sides of the triangle.
    • When solving for a missing side of a right triangle, but the only given information is an acute angle measurement and a side length, use the trigonometric functions listed below:
    • The trigonometric functions are equal to ratios that relate certain side lengths of a  right triangle.  
    • Recognize how trigonometric functions are used for solving problems about right triangles, and identify their inputs and outputs

  • Inverse Trigonometric Functions

    • Each trigonometric function has an inverse function that can be graphed.
    • Inverse trigonometric functions are used to find angles of a triangle if we are given the lengths of the sides.
    • Inverse trigonometric functions can be used to determine what angle would yield a specific sine, cosine, or tangent value.
    • To use inverse trigonometric functions, we need to understand that an inverse trigonometric function “undoes” what the original trigonometric function “does,” as is the case with any other function and its inverse.
    • We can define the inverse trigonometric functions as follows.

  • Trigonometric Limits

    • This equation can be proven with the first limit and the trigonometric identity $1 - \cos^2 x = \sin^2 x$.

  • Trigonometric Functions

    • Trigonometric functions are functions of an angle, relating the angles of a triangle to the lengths of the sides of a triangle.
    • Trigonometric functions are functions of an angle.
    • Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.
    • The most familiar trigonometric functions are the sine, cosine, and tangent .
    • Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle.

  • Defining Trigonometric Functions on the Unit Circle

    • Identifying points on a unit circle allows one to apply trigonometric functions to any angle.
    • We have already defined the trigonometric functions in terms of right triangles.
    • We have previously discussed trigonometric functions as they apply to right triangles.
    • The unit circle demonstrates the periodicity of trigonometric functions.
    • Use right triangles drawn in the unit circle to define the trigonometric functions for any angle

  • Trigonometric Substitution

    • Trigonometric functions can be substituted for other expressions to change the form of integrands and simplify the integration.
    • Trigonometric functions can be substituted for other expressions to change the form of integrands.
    • One may use the trigonometric identities to simplify certain integrals containing radical expressions (or expressions containing $n$th roots).
    • The following are general methods of trigonometric substitution, depending on the form of the function to be integrated.

  • Trigonometric Integrals

    • The trigonometric integrals are a specific set of functions used to simplify complex mathematical expressions in order to evaluate them.
    • The trigonometric integrals are a family of integrals which involve trigonometric functions ($\sin$, $\cos$, $\tan$, $\csc$, $\cot$, $\sec$).
    • The following is a list of integrals of trigonometric functions.
    • Some of them were computed using properties of the trigonometric functions, while others used techniques such as integration by parts.
    • Generally, if the function, $\sin(x)$, is any trigonometric function, and $\cos(x)$ is its derivative, then