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 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 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 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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  • 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 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 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 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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  • Q: What Is an Online Right Triangle Calculator?

    A: An online right triangle calculator is a program that calculates the unknown side lengths or angle measurements. It uses the known side length and angle measurements for its calculations.
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  • Q: What Is the Angular Momentum Equation?

    A: The angular momentum formula is L = Iw, where the variable L represents the angular momentum, I is the moment of inertia, and w is the angular velocity. Angular momentum is a physics concept defined as the amount of rotation of an object in relation to its shape, speed and mass.
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  • Q: How Do You Get Cos Theta From Sin Theta?

    A: The pythagorean trigonometric identity can be used to compute cos(θ) when sin(θ) is known. The formula is sin²(θ) + cos²(θ) = 1. Thus, cos(θ) is computed by taking the square root of (1 - sin²(θ)).
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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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  • What Is a Feasible Region?

    Q: What Is a Feasible Region?

    A: A feasible region is an area defined by a set of coordinates that satisfy a system of inequalities. The region satisfies all restrictions imposed by a linear programming scenario. The concept is an optimization technique. For example, a planner can use linear programming to determine the best value obtainable under conditions dictated by several linear equations that relate to a real-life problem.
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  • Q: What Is a Perfect Square Trinomial?

    A: A perfect square trinomial is the expanded product of two identical binomials. A perfect square trinomial is also the result that occurs when a binomial is squared. There are two general formulas for factoring a perfect square trinomial: x^2 + 2xy + y^2 = (x + y)^2, and x^2 - 2xy + y2 = (x - y)^2.
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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: 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 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 Cosine Curve?

    Q: What Is the Cosine Curve?

    A: The cosine curve is an up-down curve which starts at one and heads down until ? radians (180 degrees) and then heads up again. Plotting of the cosine of an angle against that angle measure results in a classic shape similar to a cosine curve.
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  • Q: What Is the Equation "sin X Squared"?

    A: The equation "sin x squared" may refer to the equations sin(x^2) or (sin(x))^2, which is the same as sin2(x). Using trigonometric identities, sine-squared of x can be used in the equations sin2(x) = 1/2 - 1/2 cos(2x), sin2(x) + cos2(x) = 1 and (cos(x))^2 = 1 - 2sin2(x).
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  • Q: What Are Real Life Examples of Periodic Functions?

    A: Some real life examples of periodic functions are the length of a day, voltage coming out of a wall socket and finding the depth of water at high or low tide. A periodic function is defined as a function that repeats its values in regular periods. The period is the length of time it takes for the cycle to repeat itself.
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