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.

See Full Answer
Filed Under:
  • 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.
    See Full Answer
    Filed Under:
  • 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.
    See Full Answer
    Filed Under:
  • 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.
    See Full Answer
    Filed Under:
  • 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.
    See Full Answer
    Filed Under:
  • 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.
    See Full Answer
    Filed Under:
  • 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.
    See Full Answer
    Filed Under:
  • 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.
    See Full Answer
    Filed Under:
  • 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.
    See Full Answer
    Filed Under:
  • 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.
    See Full Answer
    Filed Under:
  • 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.
    See Full Answer
    Filed Under:
  • Q: What is the antiderivative of tan(x)?

    A: The antiderivative of tan(x) can be expressed as either - ln |cos(x)| + C or as ln |sec(x)| + C. In these equations, C indicates a constant, ln is the natural logarithm function, cos indicates the function cosine and sec denotes the function secant.
    See Full Answer
    Filed Under:
  • Q: How is trigonometry used in physics?

    A: Because it has such a strong ability to explain space and the relationships between angles, trigonometry is used in almost every branch of modern physics, according to Clark University. Any field of physics that includes the use of angles or sides uses trigonometry. Some of the first fields in physics, statics and optics relied heavily on trigonometry during their pioneering stages.
    See Full Answer
    Filed Under:
  • Q: What is the sine wave equation?

    A: The general equation for a sine wave is y = Asin(B(x-C)) + D, where A and B are positive. A sinusoidal wave is any curve that can be written using that formula.
    See Full Answer
    Filed Under:
  • What is Pascal's triangle?

    Q: What is Pascal's triangle?

    A: Pascal's triangle is a geometric arrangement of binomial coefficients in a triangle. Its construction is related to the binomial coefficients by Pascal's rule. This intricate number pattern was named after Blaise Pascal, a French mathematician, although it was known about by the Chinese and studied for 500 years before Pascal.
    See Full Answer
    Filed Under:
  • Q: What is arctan(x) in math?

    A: The function arctan(x) describes the inverse tangent of x, wherein the ratio between the length of the sides opposite and adjacent to the angle can be used to determine the degrees or radian of the angle. Arctan can also be written as tan to the power of minus one.
    See Full Answer
    Filed Under:
  • 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.
    See Full Answer
    Filed Under:
  • Q: How can the equation sin(cos(-1)) be solved?

    A: To solve the equation sin(cos(-1)), first it is necessary to solve for cos(-1) and then find the sine of that value. Assuming that (-1) is given in units of radians, this equation is equal to 0.514. If (-1) is in degrees, the equation is equal to 0.017.
    See Full Answer
    Filed Under:
  • What are the six trig functions?

    Q: What are the six trig functions?

    A: The six trigonometric functions are the sine, cosine, tangent, cosecant, secant and cotangent. The functions are used to find a ratio between the sides of a right triangle when given one angle. They are used to evaluate numbers given in either degrees or radians.
    See Full Answer
    Filed Under:
  • Q: What is a tan inverse?

    A: Tan inverse is the function used to determine an angle when given the ratio between the length of the side opposite the angle over the length of the side adjacent to the angle. It is sometimes indicated by the terms "arctan" and "atan."
    See Full Answer
    Filed Under:
  • Q: What is cos 30 degrees?

    A: The cosine of 30 degrees is 0.86. It is also expressed as the square root of three divided by two. The cosine of an angle is calculated by dividing the length of the side of a right triangle adjacent to the acute angle by the length of the hypotenuse.
    See Full Answer
    Filed Under:
  • What did Pythagoras discover?

    Q: What did Pythagoras discover?

    A: Pythagoras often receives credit for the discovery of a method for calculating the measurements of triangles, which is known as the Pythagorean theorem. However, there is some debate as to his actual contribution the theorem.
    See Full Answer
    Filed Under:

Explore Geometry