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Properties of The Six Trigonometric Functions

Properties of The Six Trigonometric Functions
The properties of the 6 trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x) are discussed. These include the graph, domain, range, asymptotes (if any), symmetry, x and y intercepts and maximum and minimum points. Sine Function : f(x) = sin (x) Graph Domain: all real numbers Range: [-1 , 1] Period = 2pi x intercepts: x = k pi , where k is an integer. y intercepts: y = 0 maximum points: (pi/2 + 2 k pi , 1) , where k is an integer. minimum points: (3pi/2 + 2 k pi , -1) , where k is an integer. symmetry: since sin(-x) = - sin (x) then sin (x) is an odd function and its graph is symmetric with respect to the origin (0 , 0). intervals of increase/decrease: over one period and from 0 to 2pi, sin (x) is increasing on the intervals (0 , pi/2) and (3pi/2 , 2pi), and decreasing on the interval (pi/2 , 3pi/2). Cosine Function : f(x) = cos (x) Graph Tangent Function : f(x) = tan (x) Graph Domain: all real numbers except pi/2 + k pi, k is an integer. Graph Graph Graph More on

Basic Trigonometric Graphs Trigonometric Functions and Their Graphs: The Sine and Cosine (page 1 of 3) Sections: The sine and cosine, The tangent, The co-functions At first, trig ratios related only to right triangles. Then you learned how to find ratios for any angle, using all four quadrants. Then you learned about the unit circle, in which the value of the hypotenuse was always r = 1 so that sin(θ) = y and cos(θ) = x. Looking at the sine ratio in the four quadrants, we can take the input (the angle measure θ), "unwind" this from the unit circle, and put it on the horizontal axis of a standard graph in the x,y-plane. As you can see, the height of the red line, being the value of sin(θ) = y, is the same in each graph. If the green angle line had gone backwards, counting into negative angle measures, the horizontal graph on the right would have extended back to the left of zero. The Sine Wave When you do your sine graphs, don't try to plot loads of points. The Cosine Wave Top | 1 | 2 | 3 | Return to Index Next >>

Transformation of Trigonometric Graphs OML Search In these lessons, we will learn how Trigonometric Graphs can be transformed. the amplitude and vertical shift of Trigonometric Graphs the period and phase shift of Trigonometric Graphs Related Topics:More Trigonometric Lessons Stretching and Compressing of Graphs Amplitude of Trigonometric Functions The amplitude of a trigonometric function is the maximum displacement on the graph of that function. In the case of sin and cos functions, this value is the leading coefficient of the function. In the case of tan, cot, sec, and csc, the amplitude would be infinitely large regardless of the value of A. Period of Trigonometric Function The period of a function is the displacement of x at which the graph of the function begins to repeat. Consider y = sin x The value x = 2π is the point at which the graph begins to repeat that of the first quadrant. The general form isy = A sin Bxwhere is the amplitude and B determines the period. Solution: Since B = 2, the period is Solution: Rewrite Videos

Trigonometry Trigonometry (from Greek trigonon "triangle" + metron "measure") Want to Learn Trigonometry? Here is a quick summary. Follow the links for more, or go to Trigonometry Index Right Angled Triangle The triangle of most interest is the right-angled triangle. The right angle is shown by the little box in the corner. We usually know another angle θ. And we give names to each side: Adjacent is adjacent (next to) to the angle θ Opposite is opposite the angle θ the longest side is the Hypotenuse "Sine, Cosine and Tangent" Trigonometry is good at find a missing side or angle in a triangle. The special functions Sine, Cosine and Tangenthelp us! They are simply one side of a right-angled triangle divided by another. For any angle "θ": (Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.) Example: What is the sine of 35°? Calculators have sin, cos and tan, let's see how to use them: Example: What is the missing length here? We know the Hypotenuse We want to know the Opposite sin(45°) = 0.7071...

businessinsider 10 Secret Trig Functions Your Math Teachers Never Taught You - Roots of Unity - Scientific American Blog Network On Monday, the Onion reported that the "Nation's math teachers introduce 27 new trig functions." It's a funny read. The gamsin, negtan, and cosvnx from the Onion article are fictional, but the piece has a kernel of truth: there are 10 secret trig functions you've never heard of, and they have delightful names like "haversine" and "exsecant." A diagram with a unit circle and more trig functions than you can shake a stick at. (It's well known that you can shake a stick at a maximum of 8 trig functions.) The familiar sine, cosine, and tangent are in red, blue, and, well, tan, respectively. Whether you want to torture students with them or drop them into conversation to make yourself sound erudite and/or insufferable, here are the definitions of all the "lost trig functions" I found in my exhaustive research of original historical texts Wikipedia told me about. Versine: versin(θ)=1-cos(θ) Vercosine: vercosin(θ)=1+cos(θ) Coversine: coversin(θ)=1-sin(θ) Covercosine: covercosine(θ)=1+sin(θ)