dessskris Posted May 17, 2011 Author Report Share Posted May 17, 2011 Errrrr okay... Then? What does it infer? I can only see that it proves sin²θ + cos²θ = 1 (from Pythagoras) Does it have anything to do with: arcsin(-x) = -arcsin(x) arccos(-x) = arccos(x) ? (as I was previously asking this) If yes, how? Sorry, I am very slow... Once I get it I promise I won't ask it again. PS. You may want to use imgur.com instead of imageshack. Sometimes pictures from imageshack are unable to be seen on Firefox. I can see it though as I'm currently not using Firefox thanks! Reply Link to post Share on other sites More sharing options...
chrypton Posted May 17, 2011 Report Share Posted May 17, 2011 (edited) Errrrr okay... Then? What does it infer? I can only see that it proves sin²θ + cos²θ = 1 (from Pythagoras) Does it have anything to do with: arcsin(-x) = -arcsin(x) arccos(-x) = arccos(x) ? (as I was previously asking this) If yes, how? Sorry, I am very slow... Once I get it I promise I won't ask it again. PS. You may want to use imgur.com instead of imageshack. Sometimes pictures from imageshack are unable to be seen on Firefox. I can see it though as I'm currently not using Firefox thanks! Yeah, because arcsin is the inverse of sin. From the above illustration we can see that: and then we must have: Draw up the unit circle and try with cos and arccos and you'll see why Edited May 17, 2011 by chrypton 1 Reply Link to post Share on other sites More sharing options...
dessskris Posted May 17, 2011 Author Report Share Posted May 17, 2011 ohhh yes I get it now! I see I see. very interesting. I never knew this thank you very much! it must have been a lot of pain drawing all the shapes and all PS. If anybody has any tips on how to memorise the trig values of the special angles, apart from the special triangles method, I would be very grateful! 1 Reply Link to post Share on other sites More sharing options...
genepeer Posted May 17, 2011 Report Share Posted May 17, 2011 PS. If anybody has any tips on how to memorise the trig values of the special angles, apart from the special triangles method, I would be very grateful!I memorized the order of angles. 0 -> 30 -> 45 -> 60 -> 90 (sorry can't be bothered to put the degree signs) or 0 -> pi/6 -> pi/4 -> pi/3 -> p/2Then in the same order, for sin(theta). 1/2*sqrt(0) -> 1/2*sqrt(1) -> 1/2*sqrt(2) -> 1/2*sqrt(3) -> 1/2*sqrt(4)for cos(theta): the above list in reverse. 1/2*sqrt(4) -> ...for tan(theta): use the tan(x)=sin(x)/cos(x)To practice, at the beginning of tests/exams, you could quickly fill in this table on a rough papertheta | sin(theta) | cos(theta) | tan(theta)0...pi/6...pi/4...pi/3...pi/2... 2 Reply Link to post Share on other sites More sharing options...
dessskris Posted May 18, 2011 Author Report Share Posted May 18, 2011 Thanks Gene-Peer! That seriously helped. I need to get used to it though, used it in my semester exams but I was once confused with the radian angles.. Ahhhhh my exam was an epic failure!! Anyway... (1+z²)/(1-z²) = i z is a complex number x+iy How do we find |z| ??? I'm guessing this has got something to do with comparing the real values on both sides and imaginary values and then solve it simultaneously. But I just couldn't manage to get it!! Or is there any other method?? Thank you! Reply Link to post Share on other sites More sharing options...
genepeer Posted May 18, 2011 Report Share Posted May 18, 2011 (edited) ^ There's a division sign between the brackets.(1+z2)/(1-z2)=i1+z2=i-z2i(1+i)z2=i-1z2=(i-1)/(1+i)=i, I skipped a couple of steps here|z2| = 1|z| = 1 Edited May 18, 2011 by Gene-Peer 1 Reply Link to post Share on other sites More sharing options...
Asukers Posted May 20, 2011 Report Share Posted May 20, 2011 Sorry to change the topic! What's the purpose of the discriminant in a quadratic? I know that if discriminant > 0, there are two distinctive roots discriminant = 0, -b/2a is the only solution for x discriminant < 0, there are no real roots (as you can't get the negative of a root) buttt what's the purpose of it? What does it tell us? ...Just why do we need to know the discriminant values of the roots of a quadratic?!? Does it tell us something about the graph? Reply Link to post Share on other sites More sharing options...
dessskris Posted May 20, 2011 Author Report Share Posted May 20, 2011 @Gene-Peer OMG thanks a lot!! I substituted in z=x+yi and got some weird stuffs and not finish it so stupid.. @Asukers it's okay. just ask anything anytime when discriminant>0, there are 2 roots, meaning the curve will cut the x-axis twice. when discriminant=0, there is only 1 root, meaning the curve will only cut the x-axis once, or the curve is touching the x-axis. when discriminant<0, there are no roots, meaning the curve will not cut the x-axis. a better demonstration: Reply Link to post Share on other sites More sharing options...
Asukers Posted May 20, 2011 Report Share Posted May 20, 2011 Thank you so much! That did clarify it. So basically the discriminant plays a role in the vertical translation of a quadratic?and also, what does "distinct root" mean? Reply Link to post Share on other sites More sharing options...
timtamboy63 Posted May 20, 2011 Report Share Posted May 20, 2011 I think it means that it crosses the x axis, rather than touches? I never really understood why they did that, as when working algebraically, there's no pratical difference. Reply Link to post Share on other sites More sharing options...
Keel Posted May 20, 2011 Report Share Posted May 20, 2011 Thank you so much! That did clarify it. So basically the discriminant plays a role in the vertical translation of a quadratic?and also, what does "distinct root" mean?I think it means that it crosses the x axis, rather than touches? I never really understood why they did that, as when working algebraically, there's no pratical difference.The values of b and ac, yes.Distinct root means there is only one solution i.e. the discriminant is 0 and the function touches but does not cross the x axis. Reply Link to post Share on other sites More sharing options...
dessskris Posted May 20, 2011 Author Report Share Posted May 20, 2011 Keel, she is asking about distinct roots.when discriminant>0, the quadratic curve has two distinctive roots i.e. different roots.when discriminant=0, the quadratic curve actually still has two roots, but they are not distinctive/not different. in simpler words, it has only one same root.if it has distinct roots, the curve cuts the x-axis at two distinct points, for example the curve y=(x+3)(x-4) cuts the x-axis at (-3, 0) and at (4, 0).if it has two same roots, the curve cuts the x-axis at one same point, for example the curve y=(x-2)² cuts the x-axis at (2, 0) i.e. it touches the x-axis. Reply Link to post Share on other sites More sharing options...
Asukers Posted May 20, 2011 Report Share Posted May 20, 2011 Wow, you guys - thanks so much. I really get it now. It's these simple things that the teachers always forget to go over, at least my in school... Reply Link to post Share on other sites More sharing options...
dessskris Posted May 21, 2011 Author Report Share Posted May 21, 2011 no problem I have a question. when I woke up this morning... I randomly thought about this: arcsin(-x) = -arcsin(x) arccos(-x) = arccos(x) I know I've brought up this issue before, and people have explained it to me, but I still don't understand the 2nd one. arccos(-x) = arccos(x) I think it's not true. even when I substitute in numbers, it's not true. but I think: arccos(-x) = π-arccos(x) what do you guys think? any formal proof or explanation? thanks. Reply Link to post Share on other sites More sharing options...
Keel Posted May 21, 2011 Report Share Posted May 21, 2011 no problem I have a question. when I woke up this morning... I randomly thought about this: arcsin(-x) = -arcsin(x) arccos(-x) = arccos(x) I know I've brought up this issue before, and people have explained it to me, but I still don't understand the 2nd one. arccos(-x) = arccos(x) I think it's not true. even when I substitute in numbers, it's not true. but I think: arccos(-x) = π-arccos(x) what do you guys think? any formal proof or explanation? thanks. http://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Relationships_among_the_inverse_trigonometric_functions You will find it under the "Relationships among the inverse trigonometric functions" section. The first graph to the right demonstrates it quite well. So you were right with arccos(-x) = π-arccos(x) Reply Link to post Share on other sites More sharing options...
Schnee Posted May 21, 2011 Report Share Posted May 21, 2011 Hello guys! I'm having a bit of trouble figuring out the equations for this trig graph from my homework. I've never been that good at trig so yeah.>.> The graph increases from left to right, so I assumed it a tangent graph. We need to find 2 equations for this graph. I found the tangent equation but I'm not sure if I did it the right way: first I found the vertical displacement and the phase shift that are pretty obvious on the graph, then since a tangent graph's period is pi not 2pi like that of cosine and sine graphs, and the period on this graph is 2pi, the frequency (or B) is 1/2 Then it seems like the graph has been vertically compressed, so I found a point on the graph (8pi/9,0) and solved for the amplitude (A) my tangent equation is y=0.24tan((x+0.25pi)/2)+1 I did the same thing for the cotangent graph, but then the cotangent graph is a mirror image of the tangent graph and I can't use reflections since the graph doesn't reflect off the y-axis. So now I'm stuck with only one equation, any idea how I can find the second equation? Thanks. Reply Link to post Share on other sites More sharing options...
Guest hellokitty818 Posted May 24, 2011 Report Share Posted May 24, 2011 I have the points A(1,3,-17) and B(6,-7,8) which lie on line l. Then I was able to get the equation of the line in parametric form but then I am stuck on part b. It says that point p is on line l that OP is perpendicular to l. Find the coordinates of P. Your inputs are greatly appreciated please HELP :{ Reply Link to post Share on other sites More sharing options...
genepeer Posted May 24, 2011 Report Share Posted May 24, 2011 Use vectors. Equation for I is r= a + λb, where a is any of the vectors OA or OB and b is the the vector AB or BA.Since r is the position vector to any point on the line I (including p), and b is the direction vector of the line, you are looking for the point where r is perpendicular to b, i.e., r.b=0 (full stop for dot-product). Solve for λ, then substitute the solution into r and you've got the position vector OP. Reply Link to post Share on other sites More sharing options...
adletaY Posted May 25, 2011 Report Share Posted May 25, 2011 Just had a stats test, and I think (hope) I got everything correct except this question:A machine fills bottles with orange juice. A sample of six bottles is taken at random. The bottles contain the following amounts (in ml) of orange juice: 753, 748, 749, 752, 750, 751. Find(a) the sample standard deviation;(b) an unbiased estimate of the population standard deviation from which this sample is taken.Okay, so I put the list into my GDC, and found Sx = 1.87, which is the sample standard deviation, but apparently it's 1.71?I then did the correct process to find the unbiased estimate sqrt(n)/(n-1)* 1.87 - 2.05, but since my answer for a was wrong, that was too. Was I wrong in thinking Sx is the sample standard deviation? I thought sigmax was the population one, so I'm not sure . . . Reply Link to post Share on other sites More sharing options...
Drake Glau Posted May 25, 2011 Report Share Posted May 25, 2011 If it was an actual IB question then your 2nd question should be fine. There will likely be a followthrough meaning that you found the right answer using your previous wrong answer. All I can help you with Reply Link to post Share on other sites More sharing options...
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