Posts Tagged ‘tangent’
Tuesday, November 24th, 2009
How to Calculate the Angle of Depression
Description
A detailed tutorial on calculating the angle of depression. Step by step tutorial including several examples of the angle of depression for reference.
Overview
The angle of depression is the angle at which a person must be looking in order to see an object that is lower than the observer. Typically, the angle of elevation is a term used in trigonometry, when calculating angles of a right triangle. In a right triangle, the angle of elevation is the angle between the hypotenuse and the base, when the base of the triangle is actually located at the top of the figure. It can be calculated by using SOHCAHTOA and solving for the sine, cosine, or tangent.
Tags: angle, calculate, cosine, depression, horizontal, line, lower, object, point, right, sine, SOHCAHTOA, tangent, triangle, trig, trigonometry
Posted in Trigonometry | No Comments »
Tuesday, November 24th, 2009
How to Calculate the Angle of Elevation
Description
A detailed tutorial on how to calculate the angle of elevation. Step by step tutorial including several examples of the angle of elevation for reference.
Overview
The angle of elevation is the angle at which a person must be looking in order to see an object that is higer than the observer. Typically, the angle of elevation is a term used in trigonometry, when calculating angles of a right triangle. In a right triangle, the angle of elevation is the angle between the hypotenuse and the base. It can be calculated by using SOHCAHTOA and solving for the sine, cosine, or tangent.
Tags: angle, calculate, cosine, elevation, higher, horizontal, line, object, point, right, sine, SOHCAHTOA, tangent, triangle, trig, trigonometry
Posted in Trigonometry | No Comments »
Tuesday, November 10th, 2009
How to Find the Opposite and Adjacent Sides of a Triangle
Description
A detailed tutorial on how to find the opposite and adjacent sides of a triangle. Step by step tutorial including several examples of finding the opposite and adjacent sides of a triangle for reference.
Overview
When using SOHCAHTOA, you will often see something such as “find the opposite side” or “find the adjacent side.” Unlike the hypotenuse, the opposite and adjacent sides change depending on what angle you are working with. The right angle is found opposite the hypotenuse and you will never be working it. Tip your triangle so that your right angle is balanced across the bottom and left, and your hypotenuse crosses the right. You will be working with the angles on the top and on the bottom right. The adjacent side is one of the sides that forms your angle – one of which is the hypotenuse, so it is the other side. And to find the opposite side, draw a straight line from your angle. The line it crosses should be the one directly across from your angle, and it is the opposite side.
Tags: adjacent, angle, cosine, hypotenuse, opposite, pythagorean theorem, side, sine, SOHCAHTOA, tangent, trig, trigonometry
Posted in Trigonometry | No Comments »
Tuesday, October 20th, 2009
How to Graph the Cotangent Function
Description
A detailed tutorial on solving the graph of the cotangent function. Step by step tutorial including several examples of how to solve the graph of the cotangent function for reference.
Overview
The graph of cotangent is very closely related to the graph of tangent and the graph of x cubed. The graph occurs in periods of pi, just like the tangent function. When graphing both the cotangent function and the tangent function together, they criss-cross to form an intricate looking curve. This is because tangent and cotangent are the opposite of each other - tangent is equal to one over cotangent.
Tags: amplitude, asymptote, cotangent, function, graph, intervals, period, pi, tangent, trigonometric, trigonometry, x, y
Posted in Trigonometry | No Comments »
Tuesday, October 20th, 2009
How to Graph the Tangent Function
Description
A detailed tutorial on solving the graph of the tangent function. Step by step tutorial including several examples of how to solve the graph of the tangent function for reference.
Overview
The graph of the tangent function looks a great deal like the graph of x cubed – just repeated several times. The graph of tangent is drawn in a period of pi – meaning a “line” is put down every pi spaces for a guideline on where to draw the graph – and hits all of the major points of the graph, also in intervals of pi. There is no amplitude of the tangent function because it extends up to both negative infinity and positive infinity in vertical directions.
Tags: amplitude, asymptote, function, graph, infinity, intervals, negative, period, pi, positive, tangent, trigonometric, trigonometry, vertical, x, y
Posted in Trigonometry | No Comments »
Thursday, October 8th, 2009
An Introduction to the Law of Tangents
Description
A detailed tutorial on the Law of Tangents. Step by step tutorial including several examples of the Law of Tangents for reference.
Overview
The Law of Tangents refers to the lengths of the three sides of a triangle and the tangents of the angles. This can be used with respect to any triangle, not just right triangles. While the Law of Tangents is not as well known as the Law of Sines or the Law of Cosines, it is useful. The Law of Tangents can be used whenever either two sides and an angle, or two angles and a side, are known on any given triangle. The proof of this law starts with the Law of Sines. The Law of Tangents is as follows:
![\frac{a-b}{a+b} = \frac{\tan[\frac{1}{2}(\alpha-\beta)]}{\tan[\frac{1}{2}(\alpha+\beta)]}.](http://s.wordpress.com/latex.php?latex=%5Cfrac%7Ba-b%7D%7Ba%2Bb%7D%20%3D%20%5Cfrac%7B%5Ctan%5B%5Cfrac%7B1%7D%7B2%7D%28%5Calpha-%5Cbeta%29%5D%7D%7B%5Ctan%5B%5Cfrac%7B1%7D%7B2%7D%28%5Calpha%2B%5Cbeta%29%5D%7D.&bg=ffffff&fg=000000&s=0 "\frac{a-b}{a+b} = \frac{\tan[\frac{1}{2}(\alpha-\beta)]}{\tan[\frac{1}{2}(\alpha+\beta)]}.")
Tags: angle, ASA, law, law of cosines, law of sines, law of tangents, length, Math, right, side, SSA, tangent, tangents, triangle, trigonometry
Posted in Trigonometry | No Comments »
Tuesday, October 6th, 2009
Plotting Points in the Polar Coordinate System
Description
A detailed tutorial on plotting points in the polar coordinate system. Step by step tutorial including several examples of how to plot points on the polar coordinate system for reference.
Overview
By this point, everyone should know how to plot points on a normal graph. But what about a circular graph? This circular graph is called the polar coordinate system or the polar plane. Instead of using the points (x, y), the polar coordinate system uses the points (r, theta). Theta is a greek letter that looks like a zero with a horizontal line drawn through the center. Most of the points you will be finding for the polar coordinate system will be used with trigonometric functions – sine, cosine, and tangent. Graphing occurs in about the same way as it would on a normal graph – just match up the points, even if they are on a circle.
Tags: Calculus, circle, coordinate, cosine, function, functions, graph, Math, points, polar, r, sine, system, tangent, theta, trig, trigonometric, x, y
Posted in Calculus | No Comments »
Friday, October 2nd, 2009
Identifying the Cofunction
Description
A detailed tutorial on identifying the cofunction. Step by step tutorial including several examples of how to identify the cofunction for reference.
Overview
In math, we say that a function f is a cofunction of a function g if f(A) = g(B), and A and B are complimentary angles. Cofunctions are very often used with trigonometric functions like sine, cosine, and tangent. If you write a function in terms of its cofunction, it can make it easier to solve certain equations.
Tags: angles, cofunction, complimentary, cosecant, cosine, cotangent, function, Math, secant, sine, tangent, trigonometric function, trigonometry
Posted in Trigonometry | No Comments »
Friday, September 18th, 2009
The Tangent Rule and Formula
Description
A detailed tutorial on solving unknown lengths and angles of a triangle using Tangent.
Overview
The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent sides. The formula for tangent is:
Tags: cosine, formula, Geometry, Inside, length, Math, rule, sine, SOHCAHTOA, tangent, triangle
Posted in Geometry | No Comments »
Friday, September 18th, 2009
The Sine Rule and Formula
Description
A detailed tutorial on solving unknown lengths and angles of a triangle using Sine.
Overview
The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. The formula for sine is:
Tags: angle, cosine, formula, Geometry, Inside, length, Math, rule, sine, SOHCAHTOA, tangent, triangle
Posted in Geometry | No Comments »
