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 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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  • 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 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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  • 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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  • 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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  • 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 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 Cosine Curve?

    Q: What Is the Cosine Curve?

    A: The cosine curve is an up-down curve which starts at one and heads down until ? radians (180 degrees) and then heads up again. Plotting of the cosine of an angle against that angle measure results in a classic shape similar to a cosine curve.
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  • Q: What Is the Derivative of 2sin(x)?

    A: The derivative of 2sin(x) is 2cos(x). To compute this derivative, the derivatives of the trigonometric functions need to be memorized and the constant multiple rule applied.
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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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  • 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 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 Sine Squared Plus Cosine Squared?

    A: The sum of sine squared plus cosine squared is 1. While the sine is calculated by dividing the length of the side opposite the acute angle by the hypotenuse, the cosine is calculated by dividing the length of the side that is adjacent to the acute angle by the hypotenuse.
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  • Q: What Is the Difference Between Log and Ln?

    A: In math, the term log typically refers to a logarithmic function to the base of 10, while ln is the logarithmic function to the base of the constant e. Log is called a common logarithm, and ln is called a natural logarithm.
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  • Q: What Are Some Tips for Evaluating Logarithmic Expressions?

    A: A logarithmic expression involves at least three quantities: the base, the exponent and the argument. In the expression log10(1) = 0, 10 is the base, 0 is the exponent, and 1 is the argument. Log10(1) is equal to 0, because 10 to the power of 0 is equal to 1. In general, the expression logA(b) = c means that A to the power of c is equal to b
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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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  • Who Is the Father of Trigonometry?

    Q: Who Is the Father of Trigonometry?

    A: Many historians refer to Hipparchus as the father of trigonometry, according to the New Mexico Museum of Space History. Hipparchus was born in about 190 B.C., and he spent most of his life in Rhodes, Greece.
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  • Q: What Does Cos(2pi) Equal?

    A: Cos(2pi) is equal to 1. The cosine function, cos(x), oscillates between 1 and -1 with a period of 2pi as x varies. By definition, cos(0) = 1, and the periodicity of the function means the cosine of all multiples of 2pi (2pi, 4pi and so on) is also equal to 1.
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  • What Are the Applications of Pythagorean Theorem in Daily Life?

    Q: What Are the Applications of Pythagorean Theorem in Daily Life?

    A: A real world example of the pythagorean theorem is used when determining the diagonal viewing size of a television. The length and height of the screen are given and the diagonal must be determined to explain the viewing size of the television for the customer.
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