Graphs of Other Trigonometric Functions 4.6  TOPIC_SOLVED

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.

Graphs of Other Trigonometric Functions 4.6

Postby Raphealle on Tue Mar 31, 2009 12:32 am

The question/thing says "sketch the graph of the function. Include two full periods."

my problem is with this equation:
y = -1/2 sec X

And I don't think I'm solving it properly. My teacher said find 5 essential points. The beginning and the end and three in between....
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Postby stapel_eliz on Tue Mar 31, 2009 12:55 pm

Raphealle wrote:"sketch the graph of the function. Include two full periods."

y = -1/2 sec X

And I don't think I'm solving it properly.

You'll need to upload a scan of your work to some place like ImageBucket, and then post a link here to the graphic, in order for us to view and comment on what you've done. :wink:

Raphealle wrote:My teacher said find 5 essential points. The beginning and the end and three in between....

That's usually the best bet, actually. :clap:

The secant is the reciprocal of the cosine, so you can work from what you've learned about the cosine wave. The cosine is zero at pi/2 and at (3pi)/2. It is 1 at 0 and 2pi; it is -1 at pi. These are the five "interesting" points; the rest can be viewed as "filler" once you've learned the basic shape of the cosine wave.

Since the secant is the reciprocal of the cosine, it is -1 whenever cosine is -1, it is 1 whenever cosine is 1, and it has a vertical asymptote whenever the cosine is zero.

So look at the cosine wave. Dash in the vertical asymptotes wherever the cosine is zero. Draw the dots at -1 and 1 wherever the cosine takes on those values. Since you know that the cosine is always positive or always negative between its zeroes and is always less than or equal to 1 (in absolute value), you know that the secant has the same signs on those intervals and is always greater than or equal to 1 (in absolute value). Then, between the vertical asymptotes you've drawn, and passing through the dots you've drawn inside each interval, draw the "U" shapes for the secant's graph.

Have fun! :D
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