Question 905523: Exact Question: Give the domains of the six circular functions.
It is actually a question out of my trigonometry book and it does have the answer to the problem but I don't understand how it came out to be that answer or what to do to come to get that answer.
Here is the exact answer out the book: sine and cosine: (-∞∞); tangent and secant:{s|s≠2n+1)π/2, where n is any integer}; cotangent and cosecant: {s|s≠nπ, where n is any integer}
I thought the answers were sin = y; cos=x; tan= y/x; cos=1/y; sec=1/x; cot= x/y.
I guessing i'm wrong because I just listed the circular functions but I don't see how I could tie them in with domain.
Please help and I would like it if you could be very thorough in your answering so if I can understand why and how the answer came to be. Thank you very much because I'm really in a pinch.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Exact Question: Give the domains of the six circular functions.
It is actually a question out of my trigonometry book and it does have the answer to the problem but I don't understand how it came out to be that answer or what to do to come to get that answer.
Here is the exact answer out the book: sine and cosine: (-∞∞); tangent and secant:{s|s≠2n+1)π/2, where n is any integer}; cotangent and cosecant: {s|s≠nπ, where n is any integer}
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Sin and cos are Real on the entire circle so Domain is (-oo,oo)
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since tan is y/x and sec is r/x, these are undefined when x = 0,
That occurs at +pi/2 and (3/2)pi. So your Domain excludes those values.
Since cot = x/y and csc = r/y, these are undefined when y = 0
That occurs at 0 and pi. So your Domain excludes those values.
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Cheers,
Stan H.
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