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 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 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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  • 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 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 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 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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  • 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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  • Q: What is the integral of sin^2?

    A: The integral of sin^2 is one-half of x, minus one-eighth of the sine of 4x, plus a constant. Using mathematical notation, the integral of sine squared can be written as sin^2 x dx = 1/2 * x - 1/8 * sin(4x) + C.
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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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  • How is trigonometry used in astronomy?

    Q: How is trigonometry used in astronomy?

    A: Trigonometry is used to measure the distance to stars in the solar system, and the motion of nearby stars compared to more distant stars. The method of measuring distance in space is called trigonometric parallax.
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  • Q: How do I calculate truss angles?

    A: Calculate a truss angle by first measuring the truss's base, the horizontal piece parallel to the unit's ceiling. Look for the horizontal distance from the edge of the base to the point directly below the peak. For symmetrical trusses, this equals one half of the base's length.
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  • Q: What is a reference angle?

    A: A reference angle is an angle formed by the x-axis and the terminal side of a given angle, excluding quadrantal angles. It is a helpful tool when finding the values of trigonometric functions belonging to particular angles.
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  • What are length by width by height measurements?

    Q: What are length by width by height measurements?

    A: Measurements of length, width and height are used to find the volume of a solid figure. Volume is measured in cubic units, because three values are being multiplied to arrive at the final figure.
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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 are the properties of cosine?

    Q: What are the properties of cosine?

    A: The cosine function has several distinguishing properties. It is an even function, and it is always a real number. It is also a multiple of Pi. It is not necessary for most math students to remember all the properties of cosine. Rather, the two primary properties are that it is an even function and that it has periodicity. These are most important to commit to memory.
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  • Why can't a triangle have more than one obtuse angle?

    Q: Why can't a triangle have more than one obtuse angle?

    A: An obtuse angle is more than 90 degrees. The three angles within any triangle always equal exactly 180 degrees. If two angles are obtuse — even if they are both only 91 degrees — they add up to more than 180 degrees. Therefore, it is impossible for more than one angle in a triangle to be greater than 90 degrees.
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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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  • 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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  • 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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