Trigonometry

a tangent

First, divide 180 by pi (3.14159).
Multiply that answer by 100.
You should have approximately 5729.5779514.
This result we will refer to as the Circular Ratio.

Divide the Circular Ratio by the Radius of the curve.
The answer is The Degree Of Curvature for that curve.

Graphically: measure the angle it takes to make a curve 100 feet long.
That angle is The Degree Of Curvature for that curve.

5x-2 = 3x-6 5x = 3x - 6 +2 5x = 3x - 4 5x - 3x = -4 2x = -4 x = -2

Ratio refers to division, like difference refers to subtraction. So the ratio of 5 to 10 is 5/10 or "5 to 10" or "1 to 2", or sometimes "1 in 2". It means how much by multiplication or division some quantity relates to another.

A tangent function is a trigonometric function that describes the ratio of the side opposite a given angle in a right triangle to the side adjacent to that angle. In other words, it describes the slope of a line tangent to a point on a unit circle. The graph of a tangent function is a periodic wave that oscillates between positive and negative values.

To sketch a tangent function, we can start by plotting points on a coordinate plane. The x-axis represents the angle in radians, and the y-axis represents the value of the tangent function. The period of the function is 2π radians, so we can plot points every 2π units on the x-axis.

The graph of the tangent function is asymptotic to the x-axis. It oscillates between positive and negative values, crossing the x-axis at π/2 and 3π/2 radians. The graph reaches its maximum value of 1 at π/4 and 7π/4 radians, and its minimum value of -1 at 3π/4 and 5π/4 radians.

In summary, the graph of the tangent function is a wave that oscillates between positive and negative values, crossing the x-axis at π/2 and 3π/2 radians, with a period of 2π radians.

Third quadrant.

From the origin (0,0) and on the positive x-axis. Move an arrow/line clockwise from this axis by 135 degrees. The first 90 degrees are in the bottom right (4th)quandrant. The next 90 degrees(to 180 degrees ; includes 135) will be in the bottom left (3rd) quadrant.

NB From the positive x-axis ,moving anti-clockwise about the origin the angles are positive. When moving clockwise from the same axis the angles are negative.

The pronunciation of "nulla poena sine lege" is as follows:

Noo-la pweh-na see-neh leh-geh

Note: The pronunciation is given in an approximate manner using English phonetics. It may vary slightly depending on regional accents and pronunciation norms.

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.

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Trigonometric functions are often referred to as circular functions. This is because these functions are closely related to the geometry of circles and triangles. The six primary trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). They describe the ratios between the sides of a right triangle in relation to its angles. Trigonometric functions have numerous applications in mathematics, physics, engineering, and various other fields.

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He made his observations with very simple instruments, using an ordinary plumb-line to measure the angles of elevation of the stars. He also introduced a mathematical innovation by using Hindu-Arabic numerals in his sine tables, the first transition from the duodecimal to the decimal system.

A true bearing is a type of bearing that indicates the direction of one point relative to another point on the Earth's surface, measured using true north as a reference point. It is expressed as an angle, measured in degrees, between a fixed reference direction (such as true north) and the direction of the point being observed.

True bearings are important for navigation, surveying, and other applications that require accurate direction-finding. They differ from magnetic bearings, which are measured relative to the Earth's magnetic field, and are subject to variation depending on the location and time. True bearings are more reliable and consistent, as they are based on the Earth's axis of rotation and do not change over time or location.

YES!!!!

Sin(2x) = Sin(x+x')

Sin(x+x') = SinxCosx' + CosxSinx'

I have put a 'dash' on an 'x' only to show its position in the identity. Both x & x' carry the same value.

Hence

SinxCosx' + CosxSinx' =

Sinx Cos x + Sinx'Cosx =>

2SinxCosx

Y=mx+b is the equation of a straight line graph in mathematics. Answer Y = mX + b This is the general form of an Equation for a Straight Line when plotted on a coordinates of X versus Y. where. m = slope of the line b = intercept point of the Y-Axis (or the value of Y when X=0)

y=6

In geometry, a deltahedron (plural deltahedra) is a polyhedron whose faces are all equilateral triangles. The name is taken from the Greek upper case delta (Δ), which has the shape of an equilateral triangle.

If this is a homework question, please consider trying to answer it on your own first, otherwise the value of reinforcement of the lesson will be lost on you.

To determine the trigonometry function of sin, with a period of pi, and amplitude of 1, and a vertical shift of +1, start simple and expand.

The period of sin(x) is 2 pi, so to halve that period you need sin(2x).

The amplitude of sin(2x) is 2, so to halve that amplitude you need 1/2 sin(2x).

To shift any function up by 1, simply add 1 to it, so the final answer is 1/2 sin(2x) + 1.

Note: This is very simple when you take it step by step.

The tangent of infinity is undefined because it is not a real number. The tangent function is defined as the ratio of the side opposite a given angle to the side adjacent to the angle in a right triangle. Since infinity is an abstract concept which has no physical representation, it is not possible to measure the sides of a triangle with an infinite length. Therefore, the tangent of infinity is undefined.

they use trigonomerty for cutting angled cuts and finding a missing side

You muliply the base times the height of one of the triangles in the trianagular prism (both triangles will be similar, proportional, and equal, and you divide that number by two or multiply that number by 1/2, then you multiply that number times the height or length of one triangle's end to the other triangle's end of the triangular prism to obtain your final volume. The formula is as follows.

V=1/2(b*h)(height)

There are 360 degrees around a circle. So first find the circumference of the circle and then divide it by 360 which will give 1 degree of distance and then multiply this by 50 to show how far the spider crawled:

Circumference = 100*pi

1 degree = (100*pi)/360 = 5/18*pi

Distance crawled = 50*5/18*pi = 43.6332313 inches

Answer: 44 inches to the nearest inch.

Physicists use trigonometry whenever two or more vectors (fields, forces, momentums, etc...) interact with one another. Trigonometry is especially useful in modeling waves an, which transfer energy in a manner consistant with trigonometric functions. The same is true with oscillatory motion (like a spring bouncing up and down) and electrical current, which often varies in its strength like a spring bouncing (this is AC current).

The absolute value of something is also the square root of the square of that something. This can be used to solve equations involving absolute values.

Advantages of secant method:

1. It converges at faster than a linear rate, so that it is more rapidly

convergent than the bisection method.

2. It does not require use of the derivative of the

function, something that is not available in a number

of applications.

3. It requires only one function evaluation per iteration,

as compared with Newton's method which requires

two.

Disadvantages of secant method:

1. It may not converge.

2. There is no guaranteed error bound for the computed

iterates.

3. It is likely to have difficulty if f 0(α) = 0. This

means the x-axis is tangent to the graph of y = f (x)

at x = α.

4. Newton's method generalizes more easily to new

methods for solving simultaneous systems of nonlinear

equations.

this is nothing but its a noun