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 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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  • 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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  • 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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  • 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 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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  • 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 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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  • 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 Regents Trigonometry?

    A: Regents Algebra 2/Trigonometry is an examination administered by the New York State Education Department through the Office of State Assessment. This test is designed to test the competency of a student in the areas of algebra 2 and trigonometry.
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  • Q: What is a period of sine graph?

    A: The period of the sine graph is 2pi. Sine graph oscillates between one and minus one with a period of 2pi. When x is a multiple of pi, sin(x) = 0. For x = pi/2, 5pi/2, etc, sin(x) = 1, and for x = 3pi/2, 7pi/2, etc, sin(x) = -1.
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  • Q: What is the azimuth angle?

    A: The azimuth angle in astronomy is the arc of the horizon measured clockwise from the south point or north point of the horizon to the point on the horizon intersected by the object's line of altitude. The azimuth is measured in degrees.
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  • Q: What is cos 0 degrees equal to?

    A: The cosine of zero degrees is equal to one. The cosine is a trigonometric function that can be defined through the Pythagorean Theorem as the length of the side of a right triangle adjacent to an angle over the hypotenuse of the triangle.
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  • Q: What is the derivative of cross product?

    A: The derivative of a cross product is found through the cross product formula Dt(r(t)×q(t))=r?(x)×q(x)+r(x)×q?(x), where r and q are the cross product values. The derivative is found by plugging in the known cross product values into the formula and solving for x.
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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 are the derivatives of inverse functions?

    Q: What are the derivatives of inverse functions?

    A: The derivative of an inverse function is a calculation of the slope at a particular point of a function that acts in the reverse manner of another function. It is typically denoted as the function f(x) taken to the power of negative one, followed by an apostrophe.
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  • Q: What is the tangent secant theorem?

    A: The tangent-secant theorem states that if two secant segments share an endpoint outside of a circle, the product of one segment length and the length of its external segment equals the product of the other segment's length and the length of its external segment. It is a special subtype of another mathematical theorem: the power of a point theorem.
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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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  • How do you solve a power reduction formula?

    Q: How do you solve a power reduction formula?

    A: To solve a power-reduction formula, express it in a simplified way without exponents. For example, solve "sine to the 4th power times x" by squaring "sine squared times x." From there, further simplify by multiplying "1 minus the cosine of 2x divided by 2."
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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 an online right triangle calculator?

    A: An online right triangle calculator is a program that calculates the unknown side lengths or angle measurements. It uses the known side length and angle measurements for its calculations.
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