Trig Identity Anomaly

Subhotosh Khan said:
In the first line you wrote:

sin(30 + 120) = sin (210) ,......,How

Did you mean to write 180 instead of 120 ?
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No! I didn't mean to write 180 instead of 120. The line was copied directly from the the BBC website that I provided a link to (qv).
Please have look at that site so you can see I'm not lying, lol.
It was, clearly, some witless goon who added 30 t0 120 and came up with 210 !!!!!!
Thank you for pointing out their mistake.
I was tired at the time and didn't spot that they had made this error on the very first line!
I just plugged the numbers into the addition formula (on my calculator) as an idle doodle and was thoroughly puzzled when I got the "same" answer but with a different sign! Of course sin(150°) is, indeed, 0.5 not -0.5 just as the addition formula delivers.
I only looked at their "sin(210°) = -0.5" and thought, well that's true enough, so why is the addition formula giving me a different answer (just plugging in 30° & 120° without noticing that they had added them wrongly at the outset!)
It just never occurred to me that the BBC would post such drivel without checking their sums so I assumed I was making a mistake somewhere. I spent ages trying to figure out where I'd gone wrong too! Grrrrrrr!
Thanks again for pointing out that things didn't "add up". ???
 
30 + 120 = 150. 150 is in quadrant 2. The sine of any angle is quad 2 is positive
210 is in quad 3. The sine of any angle in quad 3 is negative.
Do you still want to say that sin(30+120) = sin(210)??

Probably 210 came up because 180- 30 = 150 and 180 + 30 = 210 (that is the reference angles are equal).
 
Steven G said:
30 + 120 = 150. 150 is in quadrant 2. The sine of any angle is quad 2 is positive
210 is in quad 3. The sine of any angle in quad 3 is negative.
Do you still want to say that sin(30+120) = sin(210)??

Probably 210 came up because 180- 30 = 150 and 180 + 30 = 210 (that is the reference angles are equal).
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Steven,

Please read response #3.
 
Steven G said:
30 + 120 = 150. 150 is in quadrant 2. The sine of any angle is quad 2 is positive
210 is in quad 3. The sine of any angle in quad 3 is negative.
Do you still want to say that sin(30+120) = sin(210)??

Probably 210 came up because 180- 30 = 150 and 180 + 30 = 210 (that is the reference angles are equal).
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Please read response #5 (and thence response #3, lol)
 
Subhotosh Khan said:
Steven,

Please read response #3.
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Thank you, Subhotosh, for taking the time to read my reply and also for pointing it out to others who don't bother to. :)
I would just like everyone to know that (unlike someone at the BBC) I can add, I do understand reference angles (& ASTC) and, having taught Maths for nearly thirty years, I'm usually very comfortable with the workings of the Trig Identities.

Unfortunately, my eyesight isn't what it used to be (an age thing), I stay up much too late at night (getting far too tired to operate on all cylinders) and, clearly, I am far too trusting an individual to question the authority of such an esteemed institution as the BBC! :rolleyes:

I have reported their error to them but have no response other than an automated email telling me someone (I hope they can add better than the author, lol) will look at my comments; I will check back occasionally to see whether they have fixed it. ;)

Cheers. :thumbup:
 
The Highlander said:
Thank you, Subhotosh, for taking the time to read my reply and also for pointing it out to others who don't bother to. :)
I would just like everyone to know that (unlike someone at the BBC) I can add, I do understand reference angles (& ASTC) and, having taught Maths for nearly thirty years, I'm usually very comfortable with the workings of the Trig Identities.

Unfortunately, my eyesight isn't what it used to be (an age thing), I stay up much too late at night (getting far too tired to operate on all cylinders) and, clearly, I am far too trusting an individual to question the authority of such an esteemed institution as the BBC! :rolleyes:

I have reported their error to them but have no response other than an automated email telling me someone (I hope they can add better than the author, lol) will look at my comments; I will check back occasionally to see whether they have fixed it. ;)

Cheers. :thumbup:
Click to expand...
I am very pleased to say that I have checked back and the BBC have now fixed their mistake so their website no longer states that:-
sin (30° + 120°)=sin210°=-0.5!

It would appear that, following the comments I submitted to the BBC they have amended the page so it now reads:-
sin (30° + 120°)=sin150°=0.5.

The newly amended page may be seen here.

One small battle won! :thumbup:?
 
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