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How do you Define the trigonometric functions and give example each?
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∙ 14y ago
- Sin: Opposite over Hypotenuse
- Cosine: Adjacent over Hypotenuse
- Tangent: Opposite over Adjacent
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∙ 14y ago
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How the exponential logarithm and trigonometric functions of variable is different from complex variable comment?
The exponential function, logarithms or trigonometric functions are functions whereas a complex variable is an element of the complex field. Each one of the functions can be defined for a complex variable.
Do inverse operation undo each other?
Usually, but not always: it depends on the domains and codomains.Any function that is many-to-one (for example all even powers, all trigonometric functions) have an inverse operation that is defined over a restricted domain. They will, therefore, return the principal value but not necessarily the original value.A couple of simple example, using the square and square root functions:(-2) squared = 4butsqrt(4) = +2, not -2.sin(150°) = 0.5butsin-1(0.5) = 30°It is, of course, possible to define the sqrt function so that it returns the negative root, but then it will not return the positive one.
How many ways can you calculate a derivative in calculus?
There are multiple rules of differentiation in calculus, and each one works best in a different situation. For example, there is the product rule, quotient rule, and power rule. These work well for polynomial functions. Trigonometric functions are differentiated in their own way. Derivatives of exponential functions (for example, 7^x), are sometimes calculated by first taking the natural log of both sides of the equation y=7^x. Piecewise functions can contain multiple types of expressions, and accordingly each piece can be differentiated using a different rule. Hope this helps!
How can you tell if functions are inverse functions?
If two functions are the inverse of each other, they reverse or undo what the other function does. To give the simplest example, addition and subtraction are inverse functions, so that if you start with 7 and add 3 you get 10, and then if you subtract 3 you are back to 7, which is what you started with, so the subtraction reverses the effect of the addtion (if you subtract the same amount, which in this example was 3).
What operation undo each other?
Inverse oprations. Here are some examples (with some values excluded where one or the other operation is not defined or where one of the functions is not uniquely defined): Addition and subtraction are inverses of each other, Multiplication and division are inverses of each other, Exponentiation and logariths are mutual inverses, Trigonometric functions and their arc equivalents are mutual inverses, Clockwise rotation and anticlockwise rotation are mutual inverses. Squaring (a non-negative number) and the principal square-root of a non-negative number.
How the exponential logarithm and trigonometric functions of variable is different from complex variable comment?
The exponential function, logarithms or trigonometric functions are functions whereas a complex variable is an element of the complex field. Each one of the functions can be defined for a complex variable.
What are the trigonometric functions and ratios?
In all there are [at least] 24 trigonometric functions and ratios. Half of these are circular and the other half are hyperbolic. Sine and Cosine are basic trigonometric funtions, abbreviated as sin and cos. Tangent is the third basic ratio defined as Sin/Cos. For each of these three, there is a corresponding reciprocal function: Sine -> Cosecant (cosec or csc) Cosine -> Secant (sec) Tangent -> Cotangent (cot). Each of the above six has an inverse function, defined on an appropriate domain. They all are named by adding the prefix "arc", for example arcsin, which is usually written as sin-1. The above are the circular functions. Each one of them has a corresponding hyperbolic equivalent. These are named by adding the suffix, "h", thus cosh, sech, arccosh [= cosh-1], etc.
Define each component an give an example?
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What is the relationship between trigonometric functions and its inverse?
The trigonometric functions and their inverses are closely related and provide a way to convert between angles and ratios of sides in a right triangle. The inverse trigonometric functions are also known as arc functions or anti-trigonometric functions. The primary trigonometric functions (sine, cosine, and tangent) represent the ratios of specific sides of a right triangle with respect to one of its acute angles. For example: The sine (sin) of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine (cos) of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent (tan) of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side. On the other hand, the inverse trigonometric functions allow us to find the angle given the ratio of sides. They help us determine the angle measure when we know the ratios of the sides of a right triangle. The inverse trigonometric functions are typically denoted with a prefix "arc" or by using the abbreviations "arcsin" (or "asin"), "arccos" (or "acos"), and "arctan" (or "atan"). For example: The arcsine (arcsin or asin) function gives us the angle whose sine is a given ratio. The arccosine (arccos or acos) function gives us the angle whose cosine is a given ratio. The arctangent (arctan or atan) function gives us the angle whose tangent is a given ratio. The relationship between the trigonometric functions and their inverses can be expressed as follows: sin(arcsin(x)) = x, for -1 ≤ x ≤ 1 cos(arccos(x)) = x, for -1 ≤ x ≤ 1 tan(arctan(x)) = x, for all real numbers x In essence, applying the inverse trigonometric function to a ratio yields the angle that corresponds to that ratio, and applying the trigonometric function to the resulting angle gives back the original ratio. The inverse trigonometric functions are useful in a variety of fields, including geometry, physics, engineering, and calculus, where they allow for the determination of angles based on known ratios or the solution of equations involving trigonometric functions. My recommendation : 卄ㄒㄒ卩丂://山山山.ᗪ丨Ꮆ丨丂ㄒㄖ尺乇24.匚ㄖ爪/尺乇ᗪ丨尺/372576/ᗪㄖ几Ꮆ丂Ҝㄚ07/
Do inverse operation undo each other?
Usually, but not always: it depends on the domains and codomains.Any function that is many-to-one (for example all even powers, all trigonometric functions) have an inverse operation that is defined over a restricted domain. They will, therefore, return the principal value but not necessarily the original value.A couple of simple example, using the square and square root functions:(-2) squared = 4butsqrt(4) = +2, not -2.sin(150°) = 0.5butsin-1(0.5) = 30°It is, of course, possible to define the sqrt function so that it returns the negative root, but then it will not return the positive one.
How do you know that the value of each angle put into a trigonometric function results in exactly one output value?
The value of each angle put into a trigonometric function results in exactly one output value, because that angle represents a single set of x and y coordinates on the ray at the end of the unit circle. Since the trigonometric functions are all defined as the ratio of x and/or y and/or 1, there can only be one output value for each angle. However, the reverse is not true. As an example, tangent is defined as sine over cosine, or y over x. This means that an angle of theta plus 180 degrees generates the same value, because y over x is the same as -y over -x.
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