Posts Tagged ‘secant’
Tuesday, October 20th, 2009
How to Graph the Cosecant Function
Description
A detailed tutorial on solving the graph of the cosecant function. Step by step tutorial including several examples of how to solve the graph of the cosecant function for reference.
Overview
The graph of cosecant is very closely related to the graph of secant. The graph appears to be many concave up and concave down curves placed in periods of 2pi. In reality, the local maximums and minimums on the graph of cosecant match up with the local maximums and minimums on the graph of sine, making it easy to line them up together. This is because sine and cosecant are the opposite of each other – sine is equal to one over cosecant.
Tags: amplitude, asymptote, cosecant, function, graph, intervals, maximum, minimum, period, pi, secant, sine, trigonometric, trigonometry, x, y
Posted in Trigonometry | No Comments »
Tuesday, October 20th, 2009
How to Graph the Secant Function
Description
A detailed tutorial on solving the graph of the secant function. Step by step tutorial including several examples of how to solve the graph of the secant function for reference.
Overview
The graph of secant is very closely related to the graph of cosecant. The graph appears to be many concave up and concave down curves placed in periods of 2pi. In reality, the local maximums and minimums on the graph of secant match up with the local maximums and minimums on the graph of cosine, making it easy to line them up together. This is because cosine and secant are the opposite of each other - cosine is equal to one over secant.
Tags: amplitude, asymptote, cosecant, cosine, function, graph, intervals, maximum, minimum, period, pi, secant, trigonometric, trigonometry, x, y
Posted in Trigonometry | 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 »
Thursday, September 17th, 2009
How to Solve the Equation of a Tangent Line
Description
A detailed tutorial on the solving of the equation of a tangent line. Step by step tutorial including several examples of how to solve the equation of a tangent line for reference.
Overview
A tangent line is the straight line to a curve at any given point that just touches the curve at that point. In a mathematical sense, at that point the tangent line is going in the same direction as the curve. To solve the equation of a tangent line, say that the curve is the graph of the function y = f(x). The point at which the tangent line intersects the curve is p = (a, f(a)). Now, take another point on the curve that is close to the line, which can be expressed as q = (a + h, f(a + h)). The secant line passes through both of these points, and the slope of the secant line is equal to the difference quotient. The difference quotient is expressed as:
Those who have already studied limits will recognize the difference quotient to be the definition of a limit function.
Tags: Calculus, curve, equation, equation of a tangent line, function, graph, limit, line, Math, secant, slope, slope of secant line, tangent
Posted in Calculus | No Comments »
Thursday, September 10th, 2009
How to Solve an Integration Problem by Trigonometric Substitution
Description
This video clearly illustrates how to solve an integration problem using trigonometric substitution. One example problem is provided in the video.
Overview
Trigonometric substitution works the same way as normal substitution, only you substitute in trigonometric functions, and each trigonometric function can only be substituted for a particular pattern. These are the patterns to watch for and what you can substitute in for them:
a^2 – x^2 uses x = a * sin(theta)
a^2 + x^2 uses x = a * tan(theta)
x^2 – a^2 uses x = a * sec(theta)
All of these also have the option of including a square root with them, but it doesn’t matter – you can use the substitution without the square root. Normally after finding the x value you will take a derivative so you have the value of dx To find other values needed,SOHCAHTOA is often used with a right triangle picture. Once all of your values have been solved for, you can plug them all back into your original equation and solve.
Tags: antiderivatives, antidifferentiation, Calculus, derivatives, differentiation, integrals, integration by substitution, Math, secant, sine, tangent, trig functions, trigonometric substitution, trigonometry
Posted in Calculus | No Comments »
Friday, September 4th, 2009
How to Solve Derivatives with Trigonometric Functions
Description
This video shows the basic trigonometric functions and their derivatives. Content is laid out in an organized and easy to follow manner.
Overview
Trigonometric functions, also known as just trig functions, are very common – they are sine, cosine, tangent, secant, cotangent, cosecant. These are derivatives that you should have memorized, because there is no good way to solve for them.
d/dx sin(x) = cos(x)
d/dx cos(x) = -sin(x)
d/dx tan(x) = sec^2(x)
d/dx sec(x) = sec(x) * tan(x)
d/dx csc(x) = -csc(x) * cot(x)
d/dx cot(x) = -csc^2(x)
Tags: Calculus, cosecant, cosine, cotangent, derivative, derivatives, differentiation, Math, secant, sine, tangent, trig, trig functions, trigonometric, trigonometric functions, trigonometry
Posted in Calculus | No Comments »
Thursday, September 3rd, 2009
Parts and Equations of Circles
Description
This video explains all the different parts of the circle, with multiple picture examples. Everything is laid out in an easy to read format and the illustrations clearly show where on the circle each part is located.
Overview
Circles are very interesting shapes in the world of geometry. There are many different parts to a circle, and many different formulas. The most common formulas are the area and the circumference formula.
Area Formula: Area = pi * radius * radius = pi * radius^2
Circumference Formula: Circumference = pi * diameter = pi * 2 * radius
The area is the area inside a circle, and the circumference is the measurement of the outside of the circle. The diameter is the width of the circle, and the radius is half of the diameter. Pi is a number that is equal to approximately 3.14.
The other parts of a circle are the sector, chord, arc, tangent, and secant. These are lines that will not show up all the time and will not always need to be acknowledged, but they do exist on the circle.
Tags: arc, area, chord, circle, circumference, diameter, Geometry, Math, pi, radius, secant, sector, tangent
Posted in Geometry | No Comments »
