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Secant GraphCovid-19 has led the world to go through a phenomenal transition . E-learning is the future today. Stay Home , Stay Safe and keep learning!!! Secant Graph : We know that sec x = 1 /cos x. The cosine function has period 2π so the ecant function has also period 2π.As secant is a reciprocal of cosine function so for some values this function is discontinuous. We know that sec x ≤ -1 or sec ≥ 1. First, we graph y = cos x and then y = sec x immediately below it. Compare the y-values in each of the 2 graphs and assure yourself they are the reciprocal of each other. ![]() _______________________________________________________________________ Phase shift in secant-graph The secant function is y= sec(bx -c) - d Period = 2π/b and phase shift = c/b vertical shift = -d Example 1 : y = sec(πx -1) b = π period =2π/b = 2π/π = 2 phase shift=c/b=1/π= 1/3.14 = 0.3184 So the graph will shift to right side by 0.3184 units. If we draw a secant curve with no shifts then the (x,y)coordinates are (0,1),(1,-1) and (2,1) After shifting the coordinates will be (0 +0.3184,1),(1.3184,-1) and (2.3184,1) _______________________________________________________________ Example 2 : y = – sec(x + π/2) + 3 Solution : Guide function: y = – cos(x + π/2) + 3 a = –1 ; b = 1 ; c = – π/2 and d = 3 period = 2π/1 = 2π phase shift = x + π/2 = 0 ⇒ x = -π/2 vertical shift =3 Now you can easily graph this. ______________________________________________________________________ 1) y = -5 sec(πx/4 - π/2)-3 2) y = 2 sec(x) 3) y = sec(x - π) 4) y = -sec(x) + 1 5) What is the period of y = −4sec(πx)? 6) Find the period and phase shift of y = -4sec(πx/4 + π/4) 7) Find the period and phase shift of y = -4sec(πx/8 + π/4) 8) What is the period of y = 2sec(x/8)? 9) Find the period and phase shift of y = sec(3x) + 4 10) What is the period of y = sec(-2x)? Graph Dictionary Home Page Covid-19 has affected physical interactions between people. Don't let it affect your learning.
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