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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  • 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 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 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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  • 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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  • 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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  • 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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  • 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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  • What is the natural log of e?

    Q: What is the natural log of e?

    A: The natural logarithm of e is equal to 1. Using mathematical notation, the equation is written as ln(e) = 1, where e is a mathematical constant known as Euler's number and is equal to about 2.72.
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  • Can a triangle have two perpendicular sides?

    Q: Can a triangle have two perpendicular sides?

    A: A triangle can have two perpendicular sides. If two sides are perpendicular, the angle they form is a right angle. A triangle can have only one right angle.
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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 the application of cos(arcsin x)?

    A: The function cos(arcsin x) can be used to determine the cosine of the side of a right triangle when only the angles surrounding it are provided. For example, for a right triangle with sides a, b and c where A is angle between sides a and c, the cos(arcsin(b/c)) is equal to the cos(A) because A is equal to arcsin(b/c).
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  • What are coterminal angles?

    Q: What are coterminal angles?

    A: Coterminal angles are angles in standard position that share the same terminal side. To find a coterminal angle, simply add or subtract 360 degrees from any angle; the result is a new angle that is coterminal to the first angle. The same can be done with radians instead of degrees; instead of adding or subtracting 360 degrees, add or subtract 2π.
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  • Q: What is the slope formula?

    A: The formula for finding the slope of a line on a coordinate plane is (y2 - y1) / (x2 - x1), where (x2, y2) and (x1, y1) represent two distinct points on the line. This is also known as "change in y over change in x" or "rise over run."
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  • Q: How do you create an Algebra 2 Trig reference sheet?

    A: To create an algebra II trig reference sheet, determine the important formulas and identities that you use most often. Place them on the sheet in an organized manner that is easy to follow. Creating a reference sheet requires knowledge of the material.
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  • Q: What are amplitude, period and phase shift?

    A: Amplitude is the factor by which a function is stretched vertically. The period of a repeating graph is the width of each repeat. The phase shift is the amount that the graph is moved horizontally.
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  • Q: What are some tips for evaluating logarithmic expressions?

    A: A logarithmic expression involves at least three quantities: the base, the exponent and the argument. In the expression log10(1) = 0, 10 is the base, 0 is the exponent, and 1 is the argument. Log10(1) is equal to 0, because 10 to the power of 0 is equal to 1. In general, the expression logA(b) = c means that A to the power of c is equal to b
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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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  • Who is the father of trigonometry?

    Q: Who is the father of trigonometry?

    A: Many historians refer to Hipparchus as the father of trigonometry, according to the New Mexico Museum of Space History. Hipparchus was born in about 190 B.C., and he spent most of his life in Rhodes, Greece.
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