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 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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  • 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 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 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 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 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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  • Q: What is the domain of arcsin?

    A: The domain of the mathematical function arcsin is -1 to 1. The domain defines the possible input value for a particular function. This means the input value for arcsin, the inverse trigonometric function of sine, is never greater than 1 and never less than -1.
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  • Q: What is the linear approximation formula?

    A: The linear approximation formula is f(x) is approximately equal to f(x0) + f'(x0) x (x - x0), where f'(x) denotes the derivative of f(x). The linear approximation formula is based on the affine function and is used in math to approximate the difference between two vector functions.
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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 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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  • What does the equation "a2 + b2 = c2" refer to?

    Q: What does the equation "a2 + b2 = c2" refer to?

    A: The equation "a2 + b2 = c2" refers to the Pythagorean theorem. With this theorem, it is possible to find the length of any side of a right triangle when given the length of the other two sides.
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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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  • 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.
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  • Q: What is the angular momentum equation?

    A: The angular momentum formula is L = Iw, where the variable L represents the angular momentum, I is the moment of inertia, and w is the angular velocity. Angular momentum is a physics concept defined as the amount of rotation of an object in relation to its shape, speed and mass.
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  • Q: How do you find the equation of the tangent line?

    A: To find the equation of a line that is tangent to a curve, you must find a line with the same slope as that point of the curve. This can be done with a graphing calculator that can give the slope at a particular point or by hand using the derivative of a curve function.
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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: What is the apex of a curve?

    A: The apex of a curve is its highest point. Geometric use of the term "apex" generally refers to solids or to shapes with corners such as triangles. In autoracing and other motor sports, the apex is the point on the track that is closest to the inside of a curve.
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  • Q: How do you determine cosine values?

    A: To determine the value of the cosine of an angle in a right triangle, divide the length of the side adjacent to the angle by the length of the hypotenuse. The hypotenuse of a right triangle is the side opposite to the right angle.
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