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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  • 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 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 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 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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  • 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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  • 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 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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  • 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 are real-life examples of quadratic equations?

    A: According to Math Is Fun, real-world examples of the quadratic equation in use can be found in a variety of situations, from throwing a ball to riding a bike. In each example, the predictive qualities of the quadratic equation can be used to assess an outcome.
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  • Q: How do you find the equation of the tangent line?

    A: To find the equation of a line that is tangent to a curve, you must find a line with the same slope as that point of the curve. This can be done with a graphing calculator that can give the slope at a particular point or by hand using the derivative of a curve function.
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  • What is a tangent line approximation?

    Q: What is a tangent line approximation?

    A: Tangent line approximation is used in calculus to approximate the values of a function based on its tangent. Tangent line approximation can be used because any curve examined closely at a particular point begins to bear similarities to a straight line, represented by the tangent.
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  • Q: How is trigonometry used in architecture?

    A: Architects use trigonometry to describe the shapes and forms of a building using numerical equations. These equations are translated easily by any contractor to reproduce the exact building the architect had in mind.
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  • Q: What is the derivative of inverse tangent?

    A: The derivative of an inverse tangent is denoted by the formula: y = tan^-1 x. Given that the function has a restricted domain of pi, its derivative is: d / dx (tan^-1 x) = 1 / (1 + x^2). This is the basic derivative of an inverse tangent, meaning that the value of x can be substituted for any angle within its domain to get an actual figure.
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  • Q: What is a sine rule?

    A: The law of sines states that, for any given triangle, the ratio of the length of a side divided by the sine of the opposite angle is equal to the same ratio of the other two sides and angles. The law of sines is part of trigonometry.
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  • Q: What is the third side of isosceles triangle called?

    A: The third side of an isosceles triangle is called the base. The triangle has a total of three sides, and the base connects the remaining two sides, which are referred to as the legs. The two legs of the isosceles triangle must be equal in length.
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  • Q: What is the derivative of cos(2)?

    A: The derivative of cos(2) is 0. The derivative of cos is -sin but, in this case, it does not matter once the chain rule and the constant rule are applied. It is also possible to simplify the expression first, which results in a constant of 0.999, and the derivative of any constant is always 0.
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  • Q: What is the integral of tan(x)?

    A: The integral of tan(x) is -ln |cos x| + C. In this equation, ln indicates the function for a natural logarithm, while cos is the function cosine, and C is a constant.
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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: What is the apex of a curve?

    A: The apex of a curve is its highest point. Geometric use of the term "apex" generally refers to solids or to shapes with corners such as triangles. In autoracing and other motor sports, the apex is the point on the track that is closest to the inside of a curve.
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  • Q: What does "tangent to the x axis" mean?

    A: A tangent line is a line that touches but does not cross the graph of a function at a specific point. If a graph is tangent to the x-axis, the graph touches but does not cross the x-axis at some point on the graph.
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