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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  • 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 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 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 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 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 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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  • Q: What is the derivative of csc(x)?

    A: The derivative of csc(x) with respect to x is -cot(x)csc(x). One can derive the derivative of the cosecant function, csc(x), by using the chain rule.
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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: 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 congruent angles?

    A: Two angles are congruent if they have the same degree of angle. For example, two 110-degree angles would be congruent even if they didn't point the same direction or had different lengths of lines. The word "congruent" comes from the Latin word "congruere," which actually means "to agree."
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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 you simplify trigonometric expressions?

    Q: How do you simplify trigonometric expressions?

    A: Simplifying trigonometric expressions is a matter of understanding the circles and triangles upon which trigonometry is based. While much of the simplification can be done geometrically, knowledge of trigonometric identities will allow an algebraic solution.
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  • Q: What does 1*tan(2*x) equal?

    A: The function of 1 * tan(2x) is equal to (2 * tan[x])/(1 - tan^2[x]). Because a value multiplied by one is equal to itself, the tangent function with the variable x can be solved using the double-angles identity rule for trigonometric 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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  • Q: What is the integral of secx?

    A: The integral of sec(x) is the natural log of the absolute value of the secant of x plus the tangent of x, added to a constant. Using mathematical notation, the function can be written as the integral of sec(x) = ln |sec x + tan x| + C.
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  • Q: What is an inclined plane wrapped around a cylinder?

    A: When an inclined plane, a type of simple machine, is wrapped around a cylinder, it forms a screw, which is another type of simple machine. Machines are mechanisms that can make work easier to do.
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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 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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