Examples of trigonometric function in the following topics:
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- 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.
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- 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.
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- 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.
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- This equation can be proven with the first limit and the trigonometric identity $1 - \cos^2 x = \sin^2 x$.
- The normalized sinc (blue, higher frequency) and unnormalized sinc function (red, lower frequency) shown on the same scale.
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- A transcendental function is a function that is not algebraic.
- Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions.
- A transcendental function is a function that "transcends" algebra in the sense that it cannot be expressed in terms of a finite sequence of the algebraic operations of addition, multiplication, power, and root extraction.
- Top panel: Trigonometric function sinθ for selected angles $\theta$, $\pi - \theta$, $\pi + \theta$, and $2\pi - \theta$ in the four quadrants.
- Bottom panel: Graph of sine function versus angle.
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- 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.
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- 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
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- Hyperbolic function is an analog of the ordinary trigonometric function, also called circular function.
- The basic hyperbolic functions are the hyperbolic sine "$\sinh$," and the hyperbolic cosine "$\cosh$," from which are derived the hyperbolic tangent "$\tanh$," and so on, corresponding to the derived functions.
- The hyperbolic functions take real values for a real argument called a hyperbolic angle.
- In complex analysis, the hyperbolic functions arise as the imaginary parts of sine and cosine.
- When considered defined by a complex variable, the hyperbolic functions are rational functions of exponentials, and are hence meromorphic.
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- In certain contexts such as higher education, scientific calculators have been superseded by graphing calculators , which offer a superset of scientific calculator functionality along with the ability to graph input data and write and store programs for the device.
- Scientific calculators are used widely in any situation where quick access to certain mathematical functions is needed, especially those such as trigonometric functions that were once traditionally looked up in tables; they are also used in situations requiring back-of-the-envelope calculations of very large numbers, as in some aspects of astronomy, physics, and chemistry.
- There are many softwares (such as Mathematica, Matlab, etc.) that allows not only numerical calculations and plotting of functions, but also helping with matrix manipulations, data manipulation, implementation of algorithms, creation of user interfaces, etc.
- A typical graphing calculator built by Texas Instruments, displaying a graph of a function $f(x)=2x^2-3$.
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- The polar coordinates $r$ and $\varphi$ can be converted to the Cartesian coordinates $x$ and $y$ by using the trigonometric functions sine and cosine:
- Given the function $f(x,y) = x^2 + y^2$, one can obtain $f(\rho, \phi) = \rho^2 (\cos^2 \phi + \sin^2 \phi) = \rho^2$ using the Pythagorean trigonometric identity, which is very useful to simplify this operation.
- Particularly in this case, you can see that the representation of the function f became simpler in polar coordinates.
- This is the case because the function has a cylindrical symmetry.
- In general, the best practice is to use the coordinates that match the built-in symmetry of the function.