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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  • 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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  • 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 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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  • 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 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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  • 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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  • 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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  • How do you use a unit circle with tangent chart?

    Q: How do you use a unit circle with tangent chart?

    A: A unit circle can help solve values for the tangent of angles 30 degrees, 45 degrees and 60 degrees. Tan (θ) = x/y, sin (θ) = y and cos (θ) = x. By substituting x and y, tan (θ) = sin (θ)/cos (θ).
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  • Q: How do you graph a hyperbola?

    A: To graph a hyperbola, find and mark the center, calculate the conjugate and transverse axes, and draw the rectangle that helps you give your hyperbola the correct shape before drawing in the curves. Once graphed, a hyperbola looks like a pair of parabolas with the vertices facing each other.
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  • Q: What are some methods for solving natural log equations?

    A: Natural log equations are solved by simplifying and rewriting the equation until the variable has been isolated on one side of the equation. At that point, a numerical value for the variable can be found and the equation is solved.
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  • Q: What is the antiderivative of tan(x)?

    A: The antiderivative of tan(x) can be expressed as either - ln |cos(x)| + C or as ln |sec(x)| + C. In these equations, C indicates a constant, ln is the natural logarithm function, cos indicates the function cosine and sec denotes the function secant.
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  • Q: When was trigonometry invented?

    A: Ancient Egyptian and Greek philosophers used an early form of trigonometry that involved calculating chords to obtain the angles of a triangle. This method was effective for Euclidean plane geometry, but the heart of trigonometry, the sine, was developed in India in the sixth century.
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  • What is the natural log of e?

    Q: What is the natural log of e?

    A: The natural logarithm of e is equal to 1. Using mathematical notation, the equation is written as ln(e) = 1, where e is a mathematical constant known as Euler's number and is equal to about 2.72.
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  • Q: What is the way to evaluate sin(arc-tan x)?

    A: Evaluating sin(arc-tan x) is a simple process that involves two steps: using a right-angled triangle to label the two sides and the angle in question, which is x, and using the Pythagoras theorem to calculate the remaining side and calculating the function from these values. Writing out the expression in words is the starting point of evaluating it. In this case, it is the sine of Arc-tan x.
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  • Q: What is a skew line?

    A: Skew lines are lines that do not exist in the same plane; therefore, they can never intersect. Skew lines do not define planes, and skew lines are not parallel.
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  • Q: How is trigonometry used in physics?

    A: Because it has such a strong ability to explain space and the relationships between angles, trigonometry is used in almost every branch of modern physics, according to Clark University. Any field of physics that includes the use of angles or sides uses trigonometry. Some of the first fields in physics, statics and optics relied heavily on trigonometry during their pioneering stages.
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  • Who is the father of trigonometry?

    Q: Who is the father of trigonometry?

    A: Many historians refer to Hipparchus as the father of trigonometry, according to the New Mexico Museum of Space History. Hipparchus was born in about 190 B.C., and he spent most of his life in Rhodes, Greece.
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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: What are amplitude, period and phase shift?

    A: Amplitude is the factor by which a function is stretched vertically. The period of a repeating graph is the width of each repeat. The phase shift is the amount that the graph is moved horizontally.
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