6.3 Graphing Trig Functions Last section we analyzed graphs, now we will graph them.
6.4.1 – Intro to graphing the trig functions
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Transcript of 6.4.1 – Intro to graphing the trig functions
• Similar to other functions, we can graph the trig functions based on values that occur on the unit circle
• For this section, we will the notation:– sin(x)– cos(x)– tan(x) – Etc…
Basic Properties
• For the input variable x, we will use values of 0 ≤ x ≤ 2π
• We will evaluate each function, just like a standard function from before– Form an ordered pair, (x, f(x)) OR (x, y)
Graphing sin(x)
• Before we can graph sin(x), lets actually fill in the different values that occur on the unit circle
Graphing cos(x)
• Before we can graph cos(x), lets actually fill in the different values that occur on the unit circle– Look at any similarities
Graphing tan(x)
• To graph tan(x), we have to consider the equation tan(x) = sin(x)/cos(x)
• Using our two tables, let’s compile a table for tan(x)
• Why are there “gaps” in the tangent function?– Where else/what ever trig functions may the
“gap” reappear
Terminology
• Periodic = a function f is said to be periodic if there is a positive number p such that f(x +p) = f(x)– When values repeat– Different x values for the same y-value
Periods
• For sin(x), cos(x), the period is 2π• For the function f(x) = sin(bx – c) or g(x) =
cos(bx – c)
• Period = 2π/|b|
• Example. Determine the period for the function f(x) = 3sin(3x – 2)
• Example. Determine the period for the function g(x) = 10cos(8x + 1)
Terminology Continued
• Amplitude = distance between the x-axis and the maximum value of the function
• For the function f(x) = asin(x) or g(x) = acos(x), the value |a| is the amplitude
• Example. Determine the amplitude for the function f(x) = 10sin(2x)
• Example. Determine the amplitude for the function g(x) = -14.2cos(9x)
Terminology, 3
• Phase Shift = a change in the starting and stopping points for the period of a function
• For the function f(x) = asin(bx – c) and g(x) = acos(bx – c);
• Phase Shift = c/b