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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  • 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 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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  • 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 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 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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  • 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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  • 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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  • Who invented trigonometry?

    Q: Who invented trigonometry?

    A: The ancient Greeks were the first to develop the conceptual framework of trigonometry. The noted Greek astronomers Hipparchus, Menelaus and Ptolomy contributed in advancing the field.
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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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  • How do you work out the area of a trapezoid?

    Q: How do you work out the area of a trapezoid?

    A: To calculate the area of a trapezoid, identify the measurements of the two parallel sides and the distance between them. Put those numbers into the formula for calculating the area of a trapezium, and solve the equation.
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  • What is a function rule in mathematics?

    Q: What is a function rule in mathematics?

    A: A function is a relationship in math between two variables, often x and y, and for every value of x there is exactly one value of y. The x value is referred to as the independent variable and the y as the dependent variable.
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  • What are the applications of pythagorean theorem in daily life?

    Q: What are the applications of pythagorean theorem in daily life?

    A: A real world example of the pythagorean theorem is used when determining the diagonal viewing size of a television. The length and height of the screen are given and the diagonal must be determined to explain the viewing size of the television for the customer.
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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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  • Q: How do you solve trigonometry problems?

    A: Successfully working through trigonometry problems requires knowledge of the properties of triangles as well as the ability to measure and understand the ratios called sine, cosine and tangent. Using equations associated with the ratios, it is possible to find the angles and lengths of right angle triangles.
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  • Q: What is sine squared plus cosine squared?

    A: The sum of sine squared plus cosine squared is 1. While the sine is calculated by dividing the length of the side opposite the acute angle by the hypotenuse, the cosine is calculated by dividing the length of the side that is adjacent to the acute angle by the hypotenuse.
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  • Q: What is the value of sin 40 degrees?

    A: The value of sin 40 degrees is 0.64278760968 as seen on a calculator. The sine, cosine and tangent are all based on the right-angled triangle and are useful calculations in trigonometry.
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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 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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  • Q: What is the Pythagorean Theorem used for?

    A: The Pythagorean Theorem is used to find the length of the hypotenuse of a right triangle, a calculation which affords many practical uses, such as within the fields of construction, land surveying and navigation. The relationship between the two legs of a right triangle and the hypotenuse, shown by the equation a2 + b2 = c2, is known as the Pythagorean triplet, and its use in ancient megalithic construction is believed to predate the discovery of writing. The ancient Egyptians used a rope marked in the Pythagorean triples of 3, 4 and 5 to create right triangles and some evidence points to a possible use by Babylonian mathematicians.
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