Trigonometry

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"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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  • 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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  • 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 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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  • 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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  • 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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  • 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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  • 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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  • How do you simplify trigonometric expressions?

    Q: How do you simplify trigonometric expressions?

    A: Simplifying trigonometric expressions is a matter of understanding the circles and triangles upon which trigonometry is based. While much of the simplification can be done geometrically, knowledge of trigonometric identities will allow an algebraic solution.
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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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  • Q: What is Pascal's Triangle used for today?

    A: Pascal's Triangle, named after French mathematician Blaise Pascal, is used in various algebraic processes, such as finding tetrahedral and triangular numbers, powers of two, exponents of 11, squares, Fibonacci sequences, combinations and polynomials. The triangle was actually invented by the Indians and Chinese 350 years before Pascal's time.
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  • Q: How is the perimeter of a parallelogram calculated?

    A: The perimeter of a parallelogram is equal to the sum of the four lengths that make up the parallelogram. Instead of adding up all four sides, a person can find the perimeter by adding the width and the height and then multiplying the sum by two.
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  • Q: What is the importance of trigonometry?

    A: Trigonometry is important to mathematics as an element of calculus, statistics and linear algebra. Outside of mathematics, it is important to physics, engineering, geography and astronomy as well as architectural design.
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  • Q: What does cosine mean?

    A: The cosine function is one of the three basic functions used in trigonometry. The cosine of a right triangle is found by taking the ratio of the length of the triangle's adjacent side over the length of the hypotenuse. In other words, divide them.
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  • Q: How is cos 4pi evaluated?

    A: There are two ways to evaluate cos 4? that will both give the answer of 1. The best ways to evaluate involve the periodicity of the cosine function and the trigonometric addition formula for cosine.
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  • Q: What is the linear approximation formula?

    A: The linear approximation formula is f(x) is approximately equal to f(x0) + f'(x0) x (x - x0), where f'(x) denotes the derivative of f(x). The linear approximation formula is based on the affine function and is used in math to approximate the difference between two vector functions.
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  • What is the phase shift formula?

    Q: What is the phase shift formula?

    A: The phase shift formula for a trigonometric function, such as y = Asin(Bx - C) + D or y = Acos(Bx - C) + D, is represented as C / B. If C / B is positive, the curve moves right, and if it is negative, the curve moves left.
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  • How is the end behavior of asymptotes of functions predicted?

    Q: How is the end behavior of asymptotes of functions predicted?

    A: The end behavior of asymptotes of functions can be predicted using either polynomial long division or synthetic division. Finding the end behavior of asymptotes is valuable in circumstances where the degree of the numerator exceeds the degree of the denominator and neither term can be canceled out. Using the process of either polynomial long division or synthetic division produces the end product of an oblique asymptote, which is a type of linear function.
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  • Q: What is the integral of cos 2x?

    A: The integral of cos(2x) is 1/2 x sin(2x) + C, where C is equal to a constant. The integral of the function cos(2x) can be determined by using the integration technique known as substitution. In calculus, substitution is derived from the chain rule for differentiation.
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  • Q: How do you convert radians to degrees?

    A: Radians and degrees are both units for measuring angles with respect to a circle. Convert radians to degrees by multiplying the number of radians by 180 and then dividing the result by pi. Express your final answer in degrees.
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