TRIGONOMETRIC FUNCTIONS Graphing And Analysis (Page 7 of 13)

Now repeat the procedure to find the right x-intercept.

 2nd CALC key. 2: menu selection.

 2nd key. Right arrow key.... (4 times) ENTER key.
 2nd key. Right arrow key.... (twice) ENTER key.
 2nd key. Left arrow key. (move the cursor near the zero) ENTER key.

Calculator screen image.

The x-intercepts for the cycle shown are approximately x = 1.75 and x = 2.17, rounding to two decimal places. Since the period is π/2, all of the zeros can be expressed as 1.75 + kπ/2 and 2.17 + kπ/2, where k is any integer.

From the graph for this cycle, we observe that the y-values will be positive if x < 1.75 or if x > 2.17, and will be negative if 1.75 < x < 2.17. Therefore, f(x) > 0 on the interval [pi/4, 1.75)U(2.17, 3pi/4] and f(x) < 0 on the interval (1.75, 2.17), approximately.

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