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Section 5.3: Trigonometric Graphs Cofunctions: We start the section by looking at an arbitrary right triangle, with legs of length a and b, with hypotenuse c. Notice that we’ll get the following six properties: sin(θ) = cos(90◦ − θ) tan(θ) = cot(90◦ − θ) sec(θ) = csc(90◦ − θ) ◦ ◦ cos(θ) = sin(90 − θ) cot(θ) = tan(90 − θ) csc(θ) = sec(90◦ − θ) A function f (x) is said to be periodic if the graph repeats itself after a certain interval. Because of co-terminal angles, all six trig functions are periodic. The graphs of the six trig functions are shown below. Exercises: 1. Determine the range of the following functions: f (x) = − sin(x) − 2 g(x) = | cos(x)| + 5 h(x) = − tan2 (x) j(x) = 3 csc(x) 15 8 is on the unit circle U corresponding to a real number t. Compute trig(t). 2. The point P − , − 17 17 3. Let P be the point on the unit circle U that corresponds to the angle t. Compute the coordinates of P , as well as trig(t) for each of the following angles: (a) t = −5π (b) t = 495◦ (c) t = −390◦