SOLUTION: I have been ill and have missed several weeks of school. I am trying to catch up now that I am home from the hospital via email. My pre-cal/trig teacher sent me several homework as

Algebra ->  Formulas -> SOLUTION: I have been ill and have missed several weeks of school. I am trying to catch up now that I am home from the hospital via email. My pre-cal/trig teacher sent me several homework as      Log On


   



Question 836438: I have been ill and have missed several weeks of school. I am trying to catch up now that I am home from the hospital via email. My pre-cal/trig teacher sent me several homework assignments, but I am so behind that I do not now how to do these problems. Can you help with this one and maybe I can use it as an example? I can use a calculator on these problems.
The problem: tan{arc tan 1/2 + arc tan 1/3]
Thank you so much!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Do you know what tan and arc tan mean ?
If not, +tan%28a%29+ is the side opposite angle +a+
divided by the side adjacent to angle +a+.
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Of course, You are always talking about a right triangle
+arc+tan%28b%29+ means " the angle whose tan is +b+.
+b+ is a number here, not an angle
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+tan%28+arc+tan%28+1%2F2+%29+%2B+arc+tan%28+1%2F3+%29+%29+
Work inside the parentheses one term at a time.
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+arc+tan%28+1%2F2+%29+
On my Casio fx-115 ES, I press [ SHIFT-tan- 1/2 = ]
That gives me +26.565+ which is the angle whose
tan is +1%2F2+
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Next I press [ SHIFT-tan-1/3 = ]
That give me +18.435+ which is the angle whose
tan is +1%2F3+
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Now add the angles:
+26.565+%2B+18.435+=+45+
At this point, you have:
+tan%28+arc+tan%28+1%2F2+%29+%2B+arc+tan%28+1%2F3+%29+%29+=+tan%28+26.565+%2B+18.435+%29+
+tan%28+26.565+%2B+18.435+%29+=+tan%28+45+%29+
This is tan of the angle 45 degrees
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Now press [ tan-45 = ]
That should give you +1+, which is the answer.
It is a number, not an angle
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Note that your calculator has to be set up for angles
and not radians in order to follow this.
Your calculator shouldn't be much different
Hope this helps