Math 140 2.6: Graphing the Six Trigonometric Functions on your Calculator Trigonometry When graphing the six trigonometric functions instead of using Standard Zoom (ZOOM 6: ZStandard) we use Trigonometric Zoom (ZOOM 7: ZTrig). See below. Trigonometric Zoom resets the viewing rectangle so that it goes from [–2 , +2 ] along the x–axis with a tick mark every /2 radians. In other words there is a marker every /2 radians along the x–axis. So counting from left to right along the x–axis we have markers at –2 , –3 /2, – , – /2, 0, /2, , 3 /2, and 2 . For x = ±2 the markers do not show because they are up against the left and right edges of the viewing rectangle. Also, the y–axis goes from [–4, +4] with a tick mark every 1 unit. (Note: 6.1522856 2 and 1.5707963 /2) Sine: y = sin x Cosine: y = cos x Tangent: y = tan x Cosecant: y = csc x Secant: y = sec x Cotangent: y = cot x BASIC Facts about the Six Trigonometric Functions Domain (–, +) (–, +) Range [–1, +1] [–1, +1] Period 2 2 Even/Odd Odd Even k 2 , x k (–, +) Odd (–, –1] [+1, +) 2 Odd Sine Cosine Tangent Cosecant Secant Cotangent , x k 2 (–, –1] [+1, +) 2 , x k (–, +) Where k is an integer, k = … , –3, –2, –1, 0, 1, 2, 3, … , x Even Odd Note that in set builder notation: o A domain or range of “all real numbers” is never written in set builder notation. We just write “”. o A domain of , x k would be: { x | x 2 2 o A domain of , x k would be: { x | x k } o A range of [–1, 1] would be: { y | y 1 } k } o A range of (–, –1] [+1, +) would be: { y | y 1 } If k is an integer, k = … , –3, –2, –1, 0, 1, 2, 3, … , then … Odd Multiples of x= k = –3 k = –2 k = –1 2 2 2 3 2 1 k=0 k=1 k=2 k=3 2 2 2 2 2 2 2 2 0 1 2 3 2 2 2 2 k Integer Multiples of x = k 6 5 2 2 3 3 4 3 2 2 2 2 2 2 2 1 2 0 2 0 0 2 3 2 2 1 4 5 2 2 2 2 6 7 2 2 3 3 Graphs of Reciprocal Trigonometric Functions Sine and Cosecant Cosine and Secant Tangent and Cotangent Comments about Other TI Calculator Models The graphical images on these handouts have been produced with the TI–84 Plus Silver Edition, which is the new calculator on the market. If you have an older model of graphing calculator, your graphs for tangent, cosecant, secant, and cotangent MAY have vertical lines in them that make them look funny. Below are the graphs for tangent and secant using the default mode settings in MODE. Notice that both of these graphs contain vertical lines where the function is undefined. Your calculator is not graphing asymptotes, but rather, connecting the dots across the view screen going across left to right. If we change the MODE setting from Connected to Dot these extra lines will disappear and the graphs will be more accurately represented.

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