Emilia1320 Posted January 24, 2015 Report Share Posted January 24, 2015 So how to differentiate the function on picture ? I know how to differentiate normal functions but I haven't been taught trigonometric ones yet. Or well, I know the derivative of sine is cosine, but how should I treat the degree number alpha (the variable here). Should I convert to radians? The r is "known" as this function is linked to the figure on the other picture (the purpose to investigate the area of the quadrangle with respect to alpha)... Sorry if this question is too messed up, I guess my trigonometry is a bit rusty at the moment and I just recently started calculus so yeah... I'm grateful for help Reply Link to post Share on other sites More sharing options...
Emmi Posted January 24, 2015 Report Share Posted January 24, 2015 f(α) = 2r2[sin(90° - α) + sin(α)]/2 = r2[sin(90° - α) + sin(α)]We can simplify this with an identity: sin(90° - α) = cos(α).The proof of the above is sin(90° - α) = sin(90°)cos(α) - cos(90°)sin(α) = 1*cos(α) - 0*sin(α) = cos(α).Rewriting f(α) gives f(α) = r2[cos(α) + sin(α)].Now differentiate with respect to α, remembering that r is kept as a constant here:df/dα = r2[-sin(α) + cos(α)] = r2[cos(α) - sin(α)]. 1 Reply Link to post Share on other sites More sharing options...
A_Happy_Monkey Posted January 24, 2015 Report Share Posted January 24, 2015 This is Pre- IB? Well, I'm screwed In my current class, the worst problem that I have encountered would be dividing fractions. This explains everything- I'm not smart, everyone around me is just illiterate. 1 Reply Link to post Share on other sites More sharing options...
Emilia1320 Posted January 24, 2015 Author Report Share Posted January 24, 2015 f(α) = 2r2[sin(90° - α) + sin(α)]/2 = r2[sin(90° - α) + sin(α)]We can simplify this with an identity: sin(90° - α) = cos(α).The proof of the above is sin(90° - α) = sin(90°)cos(α) - cos(90°)sin(α) = 1*cos(α) - 0*sin(α) = cos(α).Rewriting f(α) gives f(α) = r2[cos(α) + sin(α)].Now differentiate with respect to α, remembering that r is kept as a constant here:df/dα = r2[-sin(α) + cos(α)] = r2[cos(α) - sin(α)].Great! Thousand thanks for you I tried something with a similar idea but I didnt know about the simplification with sin(90-alpha). Actually my derivative was almost similar, but just in less simplified form. I guess I should take a look at those basic identities... This is Pre- IB? Well, I'm screwed In my current class, the worst problem that I have encountered would be dividing fractions. This explains everything- I'm not smart, everyone around me is just illiterate. Well, this is actually thing I'm doing due the personal interest on math, not because we are doing it on lessons. I didnt know what should I have called it so I put it under PRE-title as I'm pre student. Thou we are doing stuff beyond dividing fractions at least on my school :/ Reply Link to post Share on other sites More sharing options...
sushichan*-* Posted January 25, 2015 Report Share Posted January 25, 2015 I thought I was learning ahead of people in maths until I saw this post . Can i ask for your age? Reply Link to post Share on other sites More sharing options...
Emilia1320 Posted January 25, 2015 Author Report Share Posted January 25, 2015 I thought I was learning ahead of people in maths until I saw this post . Can i ask for your age?Just turned 16 in December ! 1 Reply Link to post Share on other sites More sharing options...
Emilia1320 Posted January 25, 2015 Author Report Share Posted January 25, 2015 (edited) Just turned 16 in December ! oops. i guess the "when i was your age" part in my previous post was wrong then...How old were you then? didn't you take 10th year last year (as your exams are on 2016) Haha, respect! Well, I used to hate math when I came to IB and was planning to go with studies so according to that I think I've proceeded quite all right. I'm just terrified by HL math and wanna learn as much as I can before starting it. Edited January 25, 2015 by Emilia1320 Reply Link to post Share on other sites More sharing options...
Emilia1320 Posted January 25, 2015 Author Report Share Posted January 25, 2015 How old were you then? didn't you take 10th year last year (as your exams are on 2016) Haha, respect! Well, I used to hate math when I came to IB and was planning to go with studies so according to that I think I've proceeded quite all right. I'm just terrified by HL math and wanna learn as much as I can before starting it. Just turned 15 at that point.Good luck with HL math! If you are planning/preparing/learning stuff beforehand, you obviously seem to be somewhat dedicated and interested so it won't be that bad i hope How old were you then? didn't you take 10th year last year (as your exams are on 2016) Haha, respect! Well, I used to hate math when I came to IB and was planning to go with studies so according to that I think I've proceeded quite all right. I'm just terrified by HL math and wanna learn as much as I can before starting it. Just turned 15 at that point.Good luck with HL math! If you are planning/preparing/learning stuff beforehand, you obviously seem to be somewhat dedicated and interested so it won't be that bad i hope Wow, respect yeah, I used to hate math, think I won't need it and stuff but this way people get involved in stuff they weren't before! Reply Link to post Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.