Rachel E.

asked • 03/19/17

Find the exact value of the trig function below

sin a/2 if cosa = 7/9 (assume sin a/2 is positive)

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Arthur D. answered • 03/19/17

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sin(a/2)=√(1-cosa)/2
sin(a/2)=√(1-[7/9])/2
sin(a/2)=√(2/9)/2
sin(a/2)=√(1/9)
sin(a/2)=1/3
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Kenneth S.

Arthur's work is straightforward and correct, except that I must point out that the division by two which is shown on the first line of his work MUST BE part of the radicand.  Therefore, on this WyzAnt platform, it should have been written as 

sin(a/2)=√](1-cos a)/2]

 
This is, in fact, the way he did the calculation, but the notation was was not secure, technically--i.e. it may have been do one half of the square root !
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03/19/17

Arthur D.

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Kenneth, you're absolutely right. I overlooked this. Thank you for looking over my work and thank you for the  correction for me and also for the student. As you know, the slightest mistake could throw the whole problem off. Thanks again and have a nice day.
                                                     Arthur D.
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03/20/17

Peter P. answered • 03/19/17

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Check the problem Rachel, and thank you for posting.
 
The cosine function cannot have a value anything other than something between 0 and 1, sort of like the probability ideas of the "chance" of anything happening. Some one addressed you an impossible question with no solution to start, certainly. Are you missing an inverse symbol for Arccos or something?
 
Thank you, (I hope you are not being given trick questions..)
 
Instructor Peter
 
Peter
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Rachel E.

I double (and triple) checked, that's exactly how the problem is written. Apparently the answer is 17/25, but I don't understand how they got that.
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03/19/17

Rachel E.

Oops, sorry. It's actually 1/3. But how do you get to that?
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03/19/17

Peter P.

That is another story. I will take a look and see now. One moment Rachel.
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03/19/17

Peter P.

Would you like me to walk you through the problem, or do so entirely in pre-printed step by step format?
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03/19/17

Peter P.

If we take double and half angle type trig formulas into consideration we will have to work with some square roots. Taking cos a to be equal to 1/3, will result in sin (a/2) being equal to "radical three divided by three." I could show you how, do you have any books handy to reference? Thank you Rachel.
 
-Peter P.
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03/19/17

Rachel E.

The step by step formula would be helpful. That way it will be easier to learn and use as a guide for similar problems.
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03/19/17

Peter P.

I have it worked out in pencil already if you prefer the more intelligible version of math problems not typed out with improper digital notating formats. Would you like to find a way for me to send you a paper copy or compromise on quality? It is up to you, again, thank you.
 
Peter P.
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03/19/17

Peter P.

Rachel hi this is what I was speaking about exactly and thank you Kenneth and Arthur the problem here was on all of us, originally the value of cosine Alpha was found to be 9/7 an improper fraction greater in value than Unity, a "does not exist" situation in mathematics. We should ask Rachel if she the original question was edited. Thanks everyone. And Rachel.
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03/20/17

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