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 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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  • 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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  • 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 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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  • 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 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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  • 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 is the integral of sin x 2?

    Q: What is the integral of sin x 2?

    A: The integral of sin (x * 2) is equal to -(1/2) * cos(2x) + C. The integral can be solved using the integration technique known as substitution, which is the reverse of the chain rule used in differentiation.
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  • Q: How do you find the inverse secant?

    A: The inverse secant of a non-zero real number x is equal to the inverse cosine of the quantity 1/x. Most scientific and graphic calculators have the inverse cosine function built in to the calculator.
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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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  • 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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  • What is a tangent line approximation?

    Q: What is a tangent line approximation?

    A: Tangent line approximation is used in calculus to approximate the values of a function based on its tangent. Tangent line approximation can be used because any curve examined closely at a particular point begins to bear similarities to a straight line, represented by the tangent.
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  • Q: How do you convert radians to degrees?

    A: Radians and degrees are both units for measuring angles with respect to a circle. Convert radians to degrees by multiplying the number of radians by 180 and then dividing the result by pi. Express your final answer in degrees.
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  • Q: What is arctan(2)?

    A: The arc tangent (arctan) of 2 degrees is 63.43, while the arctan of 2 radians is 1.107. The function arctan(2) can also be described as the inverse tangent and is written as tan^-1.
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  • Q: How do you get cos theta from sin theta?

    A: The pythagorean trigonometric identity can be used to compute cos(θ) when sin(θ) is known. The formula is sin²(θ) + cos²(θ) = 1. Thus, cos(θ) is computed by taking the square root of (1 - sin²(θ)).
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  • Q: When was trigonometry invented?

    A: Ancient Egyptian and Greek philosophers used an early form of trigonometry that involved calculating chords to obtain the angles of a triangle. This method was effective for Euclidean plane geometry, but the heart of trigonometry, the sine, was developed in India in the sixth century.
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  • Q: What are real-life examples of quadratic equations?

    A: According to Math Is Fun, real-world examples of the quadratic equation in use can be found in a variety of situations, from throwing a ball to riding a bike. In each example, the predictive qualities of the quadratic equation can be used to assess an outcome.
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  • How is the end behavior of asymptotes of functions predicted?

    Q: How is the end behavior of asymptotes of functions predicted?

    A: The end behavior of asymptotes of functions can be predicted using either polynomial long division or synthetic division. Finding the end behavior of asymptotes is valuable in circumstances where the degree of the numerator exceeds the degree of the denominator and neither term can be canceled out. Using the process of either polynomial long division or synthetic division produces the end product of an oblique asymptote, which is a type of linear function.
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  • 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.
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