SOLUTION: what is the exact value of csc 3600+sec(-3600)

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Question 891112: what is the exact value of csc 3600+sec(-3600)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe it's going to be undefined.

this is because csc(3600) is undefined.

sec(-3600) is equal to 1.

1 + undefined is undefined.

you can solve this graphically or by formula.

the graph of csc(3600) is shown below:

$$$

the graph of sec(-3600) is shown below:

$$$

you can see from the graph that csc(3600) is undefined.

if one part of the answer is undefined, then the whole answer is undefined as far as i know.

by formula, you would solve for csc(3600) as follows:

360 degrees is one full cycle.

if you start at 3600 degrees and keep subtracting 360 degrees until your angle is between 0 and 360 degrees, you will find that 3600 - 10 * 360) = 3600 - 3600 = 0 degrees.

csc(0) degrees is equal to 1/sin(0) degrees is equal to 1/0 which is undefined.

sec(-3600) is analyzed as follows:

you want to keep adding 360 degrees until it turns positive.

-3600 + 10*3600 = 0 degrees.

sec(-3600) is equivalent to sec(0).

sec(0) is equal to 1 / cos(0) which is equal to 1/1 which is equal to 1.

csc(3600) = undefined.
sec(-3600) = 1
csc(3600) + sec(-3600) = undefined + 1 = undefined.

the graph confirms that to the best of my knowledge.