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 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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  • 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 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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  • 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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  • 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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  • 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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  • 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.
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  • Q: How do you integrate the function "sin" using the half angle formula?

    A: The half-angle formula is used to integrate the function sine when it is taken to a power, such as sine squared and sine to the power of 6. The half-angle formula is used to eliminate exponents from the integral, stating that sin2(x) = 1/2 - (1/2) * cos(2x).
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  • Q: What are the June 2010 trig Regents answers?

    A: Answers to the June 2010 Algebra 2 and Trigonometry Regents exams are available from the New York State Department of Education's Office of State Assessment. For further study, answer keys for a variety of previous math exams are also available.
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  • Q: What is arctan of infinity?

    A: The principal value of arctan(infinity) is pi/2. Arctan is defined as the inverse tangent function on the range (-pi/2, pi/2). This means that x = arctan(y) is the solution to the equation y = tan(x), where x is defined as being between -pi/2 and pi/2.
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  • Q: What is the third side of isosceles triangle called?

    A: The third side of an isosceles triangle is called the base. The triangle has a total of three sides, and the base connects the remaining two sides, which are referred to as the legs. The two legs of the isosceles triangle must be equal in length.
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  • 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.
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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 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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  • What is the cos of 90 degrees?

    Q: What is the cos of 90 degrees?

    A: The cosine (cos) of 90 degrees is zero. This value is taken from the unit circle, a commonly used device in mathematics that assigns values to the trigonometric functions of sine and cosine.
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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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  • 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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  • Q: How do you find the derivative of sin2x?

    A: To find the derivative of a sin(2x) function, you must be familiar with derivatives of trigonometric functions and the chain rule for finding derivatives. You need scratch paper and can use a graphing calculator to check coordinates and slopes at specific values.
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