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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  • 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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  • 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 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 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 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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  • 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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  • What are some examples using sinusoidal functions in real life?

    Q: What are some examples using sinusoidal functions in real life?

    A: In the real world, sinusoidal functions can be used to describe mechanical functions such as the swinging of a pendulum or natural phenomena such as hours of daylight. Sinusoidal functions graph wave forms.
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  • What is the midline theorem?

    Q: What is the midline theorem?

    A: The midline theorem, formally known as Varignon's theorem, states that a parallelogram is formed when the midpoints of the sides of any convex quadrilateral are connected in order. The area of the Varignon parallelogram is half of the original quadrilateral.
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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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  • 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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  • How is trigonometry used in astronomy?

    Q: How is trigonometry used in astronomy?

    A: Trigonometry is used to measure the distance to stars in the solar system, and the motion of nearby stars compared to more distant stars. The method of measuring distance in space is called trigonometric parallax.
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  • Q: What is a reference angle?

    A: A reference angle is an angle formed by the x-axis and the terminal side of a given angle, excluding quadrantal angles. It is a helpful tool when finding the values of trigonometric functions belonging to particular angles.
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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 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."
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  • Q: How do you find the ratio of sec pi?

    A: If calculating the secant when using pi in radians, the ratio known as secant of pi, or sec pi, is equal to -1. The secant of pi is equivalent to 1/(cos pi).
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  • Q: What is the derivative of inverse tangent?

    A: The derivative of an inverse tangent is denoted by the formula: y = tan^-1 x. Given that the function has a restricted domain of pi, its derivative is: d / dx (tan^-1 x) = 1 / (1 + x^2). This is the basic derivative of an inverse tangent, meaning that the value of x can be substituted for any angle within its domain to get an actual figure.
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  • Q: What is the derivative of inverse sine?

    A: The derivative of the inverse sine of x with respect to x is 1/sqrt(1-x^2), where "sqrt" stands for square root. Inverse sine of x is sometimes written as arcsin(x). By definition, arcsin(x) = -iln(ix + sqrt(1-x^2)), where i is the square root of -1 and ln is the natural logarithm.
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