Download Section 5.3: Trigonometric Graphs Cofunctions: We start the section

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)
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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)
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is on the unit circle U corresponding to a real number t. Compute trig(t).
2. The point P − , −
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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◦