Trigonometry

A:

"Plane trigonometry" is a branch of mathematics that focuses on the relationship between the sides and angles of a triangle. Plane trigonometry builds upon the basic concepts of Euclidean geometry, and it has applications in a variety of mathematical fields, from physics to advanced calculus.

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  • How do you draw a parabolic curve?

    Q: How do you draw a parabolic curve?

    A: According to the University of California, San Diego (UCSD), a parabolic curve, or "parabola," is the graphical representation of a quadratic equation. To draw one, the points of a function are plotted on an x-y coordinate grid and the plotted points are connected in succession. The solution should look similar to the bottom half of a circle.
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  • What is the definition of "plane trigonometry"?

    Q: What is the definition of "plane trigonometry"?

    A: "Plane trigonometry" is a branch of mathematics that focuses on the relationship between the sides and angles of a triangle. Plane trigonometry builds upon the basic concepts of Euclidean geometry, and it has applications in a variety of mathematical fields, from physics to advanced calculus.
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  • How is trigonometry used in aviation?

    Q: How is trigonometry used in aviation?

    A: Trigonometry is used in aviation extensively, both in the calculations performed by the machines and computers used by the pilots, and by pilots performing quick rudimentary calculations and estimates themselves. Trigonometry and trigonometric functions are used to estimate distances and landing patterns and navigate around obstacles.
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  • Who are the mathematicians who contributed to trigonometry?

    Q: Who are the mathematicians who contributed to trigonometry?

    A: Trigonometry developed in many parts of the world over thousands of years, but the mathematicians who are most credited with its discovery are Hipparchus, Menelaus and Ptolemy. Isaac Newton and Euler contributed developments to bring trigonometry into the modern age.
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  • How do I calculate the incline of a treadmill?

    Q: How do I calculate the incline of a treadmill?

    A: The incline of a treadmill in degrees is not the same as the gradient, which is given in percentage, and some treadmills do not display either figure. Calculate the incline of your treadmill on your own with a measuring tape and a calculator.
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  • What are complementary angles in real life?

    Q: What are complementary angles in real life?

    A: When it is three o’clock, the two hands of the clock are on digits 12 and 3. The seconds hand moves between these two digits and forms a pair of complementary angles in real life. The sum of the two angles formed by the seconds hand is always 90 degrees.
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  • What are the branches of trigonometry?

    Q: What are the branches of trigonometry?

    A: The two main branches of trigonometry are plane trigonometry and spherical geometry. Trigonometry in general deals with the study of the relationships involving the lengths of angles and triangles.
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  • What is a line through a circle called?

    Q: What is a line through a circle called?

    A: The line that intersects a circle can be called a diameter, a secant or a chord. The proper term depends on the line's properties and where the line intersects the circle.
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  • Does an isosceles triangle have rotational symmetry?

    Q: Does an isosceles triangle have rotational symmetry?

    A: An isosceles triangle could have rotational symmetry if it were also an equilateral triangle. An isosceles triangle is a triangle with at least two equal sides. An equilateral triangle is a triangle with exactly three equal sides. By definition, all equilateral triangles are also isosceles triangles.
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  • Q: What is the difference between log and ln?

    A: In math, the term log typically refers to a logarithmic function to the base of 10, while ln is the logarithmic function to the base of the constant e. Log is called a common logarithm, and ln is called a natural logarithm.
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  • Q: What is sine squared plus cosine squared?

    A: The sum of sine squared plus cosine squared is 1. While the sine is calculated by dividing the length of the side opposite the acute angle by the hypotenuse, the cosine is calculated by dividing the length of the side that is adjacent to the acute angle by the hypotenuse.
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  • What are some real world applications of trigonometry?

    Q: What are some real world applications of trigonometry?

    A: Trigonometry is often used in real world applications, such as astronomy, architecture, engineering, music theory and geography. Trigonometry was originally developed for geography and astronomy.
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  • Q: What is the derivative of arcsin?

    A: The derivative of arcsine is equal to one divided by the square root of one minus x squared. In mathematical terms, the function is defined as d/dx arcsine(x) = 1/sqrt(1 - x^2).
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  • Q: How do you find the ratio of sec pi?

    A: If calculating the secant when using pi in radians, the ratio known as secant of pi, or sec pi, is equal to -1. The secant of pi is equivalent to 1/(cos pi).
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  • Q: What are some common antiderivatives of trig functions?

    A: The antiderivative of the cosine function is sin x + c, and the antiderivative of the sine function is -cos x + c. The antiderivative of the tangent function is equal to ln |sec x| + c. The antiderivative is also known as the integral.
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  • Q: What is the Pythagorean Theorem used for?

    A: The Pythagorean Theorem is used to find the length of the hypotenuse of a right triangle, a calculation which affords many practical uses, such as within the fields of construction, land surveying and navigation. The relationship between the two legs of a right triangle and the hypotenuse, shown by the equation a2 + b2 = c2, is known as the Pythagorean triplet, and its use in ancient megalithic construction is believed to predate the discovery of writing. The ancient Egyptians used a rope marked in the Pythagorean triples of 3, 4 and 5 to create right triangles and some evidence points to a possible use by Babylonian mathematicians.
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  • Q: What is the integral of secx?

    A: The integral of sec(x) is the natural log of the absolute value of the secant of x plus the tangent of x, added to a constant. Using mathematical notation, the function can be written as the integral of sec(x) = ln |sec x + tan x| + C.
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  • Q: How do you calculate magnitude and direction?

    A: Vectors are important tools used to illustrate movement and elements, such as force in physics. In order to work with vectors, you have to understand how to find their direction and magnitude. In many cases, materials like grid paper, a protractor, a ruler, and a calculator are necessary.
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  • Q: How do you find the cos inverse?

    A: The basic trigonometric functions sine, cosine, and tangent give the ratio between two sides of a triangle with a given angle. The inverse trig functions find the angle if the ratio is known. Finding the inverse cosine often requires a calculator and more than five minutes if the side lengths are not given.
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  • Q: What is an application of trigonometry?

    A: One application of trigonometry in the real world is determining the distance and location of faraway objects. This is useful in navigation and in surveying. Historically, trigonometry was also applied to determine the position of heavenly bodies, but this use has been supplanted by linear algebra in modern times.
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  • How do engineers use trigonometry?

    Q: How do engineers use trigonometry?

    A: Engineering is an extremely mathematics-intensive career, with necessary skills in both trigonometry and calculus to describe mechanical designs and to make aesthetic designs practical. The understanding of angles and planes is the most common skill used by engineers. Trigonometry also contains an understanding on natural laws and mathematical expressions that can be used to assist in engineering.
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