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How do you confirm this trig identity?
sin^5 2x = 1/8 sin2x (cos(8x) - 4 cos(4x)+3)
Find the range of trigonometric points?
The range of the circular trig functions sin and cos is is [-1,1], but even in the case of circular functions the range of the tangent function is all real numbers. This is of course true of tangent even if we do not limit it to circular functions. So your question, I assume, is asking about all trig functions. If so the range is all real numbers.
What is cosine of 23 degree angle?
This can be done on a graphing calculator by making sure you have your calculator in degrees mode, and then tentering the cos(23). You get an answer of 0.9205048535.
What is the reciprocal function of sec A?
The answer is cos A . cos A = 1/ (sec A)
How do you simplify csc theta cot theta?
There are 6 basic trig functions.sin(x) = 1/csc(x)cos(x) = 1/sec(x)tan(x) = sin(x)/cos(x) or 1/cot(x)csc(x) = 1/sin(x)sec(x) = 1/cos(x)cot(x) = cos(x)/sin(x) or 1/tan(x)---- In your problem csc(x)*cot(x) we can simplify csc(x).csc(x) = 1/sin(x)Similarly, cot(x) = cos(x)/sin(x).csc(x)*cot(x) = (1/sin[x])*(cos[x]/sin[x])= cos(x)/sin2(x) = cos(x) * 1/sin2(x)Either of the above answers should work.In general, try converting your trig functions into sine and cosine to make things simpler.
Concepts of inverse trignometric?
I think you mean the concept of inverse trig functions.Let's just look at one, the inverse cosine function.cos-1 (x) also called arccos(x) is the inverse of cos(x).cos-1 (x) x=cos (theta)So to evaluate an inverse trig function we are ask what angle, theta, did we plug into the trig function (regular, not inverse function) to get x.So here is one more example.tan-1 (x) means x=cos (theta)
Sine divided by cosine?
Trig identity... sin/cos = tangent
What are the ways on how to solve trigonometric equations?
Generalities.A trig equation contains one or many trig functions of the variable arc x. Solving for x means finding the values of the trig arcs x whose trig functions make the equations true.Example of trig equations:sin (x + Pi/3) = 0.75 ; sin 2x + cos x = 1 ; tan x + 2 cot x = 3 ; tan x + cot x = 1.732.sin x + sin 3x = 1. 5 ; sin x + sin 2x + sin 3x = cos x + cos 2x + cos 3x ;The answers, or values of the solution arcs x, are expressed in terms of radians or degrees:x = Pi/3 ; x = 137 deg. ; x = 2Pi/3 + 2k.Pi ; x = - 17. 23 deg. ; x = 360 deg.The Trig Unit CircleIt is a circle with radius R = 1 unity, and with an origin O. This unit circle defines all trig functions of the variable arc x that rotates counterclockwise on it.When the arc AM, with value x, rotates on the unit circle,The horizontal axis OAx defines the trig function f(x) = cos x.The vertical axis OBy defines the trig function f(x) = sin x.The vertical axis AT defines the trig function f(x) = tan x.The horizontal axis BU defines the trig function f(x) = cot xThe trig unit circle will be used as proofs for solving basic trig equations and trig inequalities.The periodic property of all trig functions.All trig functions are periodic meaning they come back to the same values when the arc x completes one period of rotation on the trig unit circle.Examples:The trig functions f(x) = sin x and f(x) = cos x have 2Pi as periodThe trig function f(x) = tan x and f(x) = cot x have Pi as period.Find the arcs whose trig functions are known.You must know how to find the values of the arcs when their trig functions are known. Conversion values are given by calculators or trig tables.Example: After solving, you get cos x = 0.732. Calculators (or trig table) gives x = 42.95 deg.. The Unit Circle will give an infinity of other arcs x that have the same cos value. These values are called extended answers.Example: Get sin x = 0.5. Trig table gives x = Pi/6. The unit circle give an infinity of extended answers.Concept for solving trig equations.To solve a trig equations, transform it into one or many basic trig equations.Basic trig equations.There are 4 of them. They are also called "trig equations in simplest form".sin x = a ; cos x = a (a is a given number)tan x = a ; cot x = aSolving basic trig equations.The solving method proceeds by considering the various positions of the variable arc x, rotating on the trig circle, and by using calculators (or trig tables).Example 1. Solve sin x = 0.866Solution. There are 2 answers given by calculators and the trig circle:x = Pi/3 ; x = 2Pi/3 (answers)x = Pi/3 + 2k.Pi ; x = 2Pi/3 + 2k.Pi (extended answers)Example 2. Solve cos x = 0.5Solution. 2 answers given by the trig table and the trig circle:x = 2Pi/3 ; x = - 2Pi/3 (answers)x = 2Pi/3 + 2k.Pi ; x = -2Pi/3 + 2k.Pi (extended answers)Note. The answer x = - 2Pi/3 can be replaced by x = 2Pi - 2Pi/3 = 4Pi/3.How to transform a given trig equation into basic trig equations.You may use:- common algebraic transformations, such as factoring, common factor, polynomials identities....- definitions and properties of trig functions...- trig identities (the most needed)Common Trig Identities.There are about 31 of them. Among them, the last 14 identities, from #19 to #31, are called "Transformation Identities" since they are necessary tools to transform a given trig equation into many basic ones. See book titled "Solving trig equations and inequalities" (Amazon e-book 2010)Examples of trig identities: sin^2 a + co^2 a = 1 ; sin 2a = 2sin a.cos a ;1 - cos 2a = 2 sin^2 a ; cos a = (1 - t^2)/(1 + t^2)Methods to solve trig equations.There are 2 common methods to solve a trig equation, depending on transformation possibilities.Method 1. Transform it into a product of many basic trig equations, by usingcommon transformation tools or by using trig identities.Example 3. Solve 2cos x + sin 2x = 0.Solution. Replace sin 2x by 2sin x.cos x (Trig Identity #10)2cos x + sin 2x = 2cos x + 2sin x.cos x = 2cos x(1 + sin x).Next, solve the 2 basic trig equations: cos x = 0 and sin x + 1 = 0.Example 4. Solve cos x + cos 2x + cos 3x = 0.Solution. Using trig identity #26, transform it into a product of 2 basic trig equations: cos 2x (2 cos x + 1) = 0. Next, solve the 2 basic trig equations: cos 2x = 0 and cos x = -1/2.Method 2. If the trig equation contains many trig functions, transform it into an equation that contains only one trig function as a variable.Example 5. Solve 3cos ^2 x - 2sin^2 x = 1 - 3sin xTransform the equation into the one containing only sin x. Replace cos^2 x = 1 - sin^2 x (Trig Identity 1). Call sin x = t.3(1 - sin^2 x) - 2sin^2x +3sin x - 1 = 03 - 3t^2 - 2t^2 + 3t - 1 = -5t^2 + 3t + 2 = 0.This is a quadratic equation with 2 real roots 1 and -2/5. Next solve the 2 trig basic equations: sin x = t = 1 and sin x = t = -2/5.The common period of a trig equation.The common period of a given trig equation must equal the least multiple of all the contained trig functions' periods.Example: The equation cos x + tan x = 1 has 2Pi as common period.The equation f(x) = sin 2x + cos x = 0 has 2Pi as common periodThe equation sin x + cos x/2 has 4 Pi as common period.Unless specified, a trig equation must be solved covering at least one common period.Solving special types of trig equations.There are a few special types of trig equations that require specific transformations.Examples: asin x + bcox x = ca(sin x + cos x) +bsin x.cos x = casin^2 x + bsin x.cos x + c cos^2 x = 0.Checking answers.Solving trig equation is a tricky work that easily leads to errors and mistakes. The answers should be carefully checked.After solving, you may check the answers by using graphing calculators. To know how, see the book mentioned above.(This article was written by Nghi H. Nguyen, the co-author of the new Diagonal Sum Method for solving quadratic equations)
What are the important points you are to use in graphing the cosine function?
The basic cosine function is bounded by -1 and 1. It is a periodic function with a period of 2*pi radians (360 degrees). cos(0) = 1, cos(pi/2) = 0, cos(pi) = -1, cos(3pi/2) = 0, cos(pi) = 1. In between these values it forms a smooth curve. Also, it may help to understand that when the curve crosses the x-axis, its slope is 1 or -1.
How do you confirm this trig identity?
sin^5 2x = 1/8 sin2x (cos(8x) - 4 cos(4x)+3)
Why is cos an even function?
An even function is one where f(x) = f(-x) For cosine, cos(x) = cos(-x), thus cosine is an even function.
Cos x equals -cos x plus 1?
No, but cos(-x) = cos(x), because the cosine function is an even function.
Why does cos x equal cos -x?
cos x equals cos -x because cos is an even function. An even function f is such that f(x) = f(-x).
What is cos on a scientific calculator?
Short for cosine. Check this site out for detailed info. http://www.clarku.edu/~djoyce/trig/
What is mean by non-sinusoidal load?
A load that is not sinusoidally varying (i.e. resembling that of a graph of the function sin(x) or cos(x)). This means the load is not cycling or periodic so it does not repeat itself over and over - which is exactly what the graph of the trig function sin(x) demonstrates.
What is mean by non sinusoidal load?
A load that is not sinusoidally varying (i.e. resembling that of a graph of the function sin(x) or cos(x)). This means the load is not cycling or periodic so it does not repeat itself over and over - which is exactly what the graph of the trig function sin(x) demonstrates.
What is cos of a negative angle?
The cosine function is an even function which means that cos(-x) = cos(x). So, if cos of an angle is positive, then the cos of the negative of that angle is positive and if cos of an angle is negative, then the cos of the negative of that angle is negaitive.
