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GRAPHS of Trig. Functions GRAPHS of Trig. Functions We will primarily use the sin, cos, and tan function when graphing. However, the graphs of the other functions sec, csc, and cot will be covered. GRAPHS of Trig. Functions Let’s begin with the cos x function. We can generate our values for the graph using our unit circle. Generally, you will graph from -2 pi to +2 pi. GRAPHS of Trig. Functions Let’s begin with the cos x function. We can generate our values for the graph using our unit circle. Generally, you will graph from -2 pi to +2 pi. f ( x) cos x 1 2 3 3 2 2 2 2 2 1 GRAPHS of Trig. Functions Let’s begin with the cos x function. We can generate our values for the graph using our unit circle. Generally, you will graph from -2 pi to +2 pi. f ( x) cos x 1 2 3 3 2 2 2 2 2 1 cos 2 1 7 3 cos 0.7071 cos 0.7071 4 4 3 cos 0 cos 0 2 2 5 cos 0.7071 cos 0.7071 4 4 cos 1 cos0 1 GRAPHS of Trig. Functions Let’s begin with the cos x function. We can generate our values for the graph using our unit circle. Generally, you will graph from -2 pi to +2 pi. f ( x) cos x 1 2 3 3 2 2 2 2 2 1 cos 2 1 3 5 7 cos 0.7071 cos 0.7071 cos 0.7071 cos 0.7071 4 4 4 4 3 3 cos 0 cos 0 cos 0 cos 0 2 2 2 2 3 7 5 cos 0.7071 cos 0.7071 cos 0.7071 cos 0.7071 4 4 4 4 cos0 1 cos 1 cos2 1 cos 1 GRAPHS of Trig. Functions Let’s look at the sin function. Again, I generated values using the unit circle. f ( x) sin x 1 2 3 3 2 2 2 2 2 1 cos 2 1 3 5 7 cos 0.7071 cos 0.7071 cos 0.7071 cos 0.7071 4 4 4 4 3 3 cos 0 cos 0 cos 0 cos 0 2 2 2 2 3 7 5 cos 0.7071 cos 0.7071 cos 0.7071 cos 0.7071 4 4 4 4 cos0 1 cos 1 cos2 1 cos 1 GRAPHS of Trig. Functions The tangent function is different than sin and cosine. The tangent function has asymptotes that occur at certain values of pi because the function is undefined at that value. GRAPHS of Trig. Functions The tangent function is different than sin and cosine. The tangent function has asymptotes that occur at certain values of pi because the function is undefined at that value. sin x tan x cos x GRAPHS of Trig. Functions The tangent function is different than sin and cosine. The tangent function has asymptotes that occur at certain values of pi because the function is undefined at that value. sin x tan x cos x sin 2 tan 2 cos 2 GRAPHS of Trig. Functions The tangent function is different than sin and cosine. The tangent function has asymptotes that occur at certain values of pi because the function is undefined at that value. sin x tan x cos x sin 2 tan 2 cos 2 1 tan This is undefined… 2 0 Tangent is undefind for x 2 GRAPHS of Trig. Functions The tangent function is different than sin and cosine. The tangent function has asymptotes that occur at certain values of pi because the function is undefined at that value. sin x tan x cos x sin 2 tan 2 cos 2 1 tan 2 0 Tangent is undefind for x 3 3 2 2 2 2 2 GRAPHS of Trig. Functions The tangent function is different than sin and cosine. The tangent function has asymptotes that occur at certain values of pi because the function is undefined at that value. sin x tan x cos x sin 2 tan 2 cos 2 1 tan 2 0 Tangent is undefind for x 3 3 2 2 2 2 2 GRAPHS of Trig. Functions The cotangent function is similar to its cousin tangent as it too has asymptotes that occur at certain values of pi because the function is undefined at that value. cos x cot x sin x GRAPHS of Trig. Functions The cotangent function is similar to its tangent cousin. The cotangent function also has asymptotes that occur at certain values of pi because the function is undefined at that value. cos x cot x sin x cos cot sin cot 1 0 GRAPHS of Trig. Functions The cotangent function is similar to its tangent cousin. The cotangent function also has asymptotes that occur at certain values of pi because the function is undefined at that value. cos x cot x sin x cos cot sin cot 1 0 Tangent is undefind for x 2 2 GRAPHS of Trig. Functions The cotangent function is similar to its tangent cousin. The cotangent function also has asymptotes that occur at certain values of pi because the function is undefined at that value. cos x cot x sin x cos cot sin cot 1 0 Tangent is undefind for x 2 2 GRAPHS of Trig. Functions I will leave the secant and cosecant graphs for you to research. Google them if you have to. Your assignment will be to find their graphs, determine the values where they are undefined, find the range of both functions, and at what intervals their asymptotes occurs.