@@ZoradanHawk It depends on how you draw the graph of y=x. No one can graph the equations accurately enough to use the sight to make such claims. Remember we can only sketch the graph of the equations with the limitations of our eyes and the thickness of the drawing tools. In math, it has be analytically proved. Have you seen any mathematician who proves with just drawing? Mr. Woo lacks the mathematic knowledge. His videos have many errors. He does not appear to have even master's degree in mathematics. There is a reason why colleges require at least master's degree in mathematics for instructors who teache the precalculus and calculus series.
@@thomaskim5394 We know it because of the Maclaurin expansions of sinx and tanx. Just because he doesn't teach it to this class doesn't mean that he doesn't know it. I see no error in this, he's just not providing a rigours proof as the work needed for this hasn't been taught to the students at this point.
@@tg509 I already mentioned that in his earlier video. Also, there are other ways to prove without using the series. He could use the proof that only requires precalculus. What he did here is incomplete with gaps that need to be proved. In mathematics, that is not acceptable. For example, Riemann hypothesis is not considered to be proved since we still have a gap that needs to be proved.
@@thomaskim5394 - This is highschool math. If he used the rigor you're demanding at this stage, everyone would be lost in the details. Besides, the statement you referenced is irrelevant to the lesson (at least up to this point).
Hey there! First of all, transform the equation of the tangent in explicit form. That would be: y=(-5/k)x-78/k. Therefore the coefficient (slope) m=-5/k, and n=-78/k. Since this is a central equation of a circle, the centre has coordinates S(0,0) and the radius is 6. The connection between these two is expressed with the formula (m*p-q+n)^2=r^2(m^2+1). Where as p and q are the coordinates of the centre of the circle - both 0. So if we use the numbers in the formula it be like this: (-5/k*0-0-78/k)^2=36(25/k^2+1). Now you have an equation with 1 variable k. I hope i helped, if you have any questions feel free to text me..
Great video! Which age-group is the class in?
thank u
For specifically this question though why not just leave your calculator in deg and do 1000sin(5) and be done with higher accuracy?
Try The RMO 2018 paper
How do you know the graph shows sin theta is slightly less than theta and tan theta is slightly more than theta for small theta?
Cause when you start to get away from the origin, you see that line y=x is 1) slightly above y=sinx, and 2) slightly below y=tanx.
@@ZoradanHawk It depends on how you draw the graph of y=x. No one can graph the equations accurately enough to use the sight to make such claims. Remember we can only sketch the graph of the equations with the limitations of our eyes and the thickness of the drawing tools. In math, it has be analytically proved. Have you seen any mathematician who proves with just drawing? Mr. Woo lacks the mathematic knowledge. His videos have many errors. He does not appear to have even master's degree in mathematics. There is a reason why colleges require at least master's degree in mathematics for instructors who teache the precalculus and calculus series.
@@thomaskim5394 We know it because of the Maclaurin expansions of sinx and tanx. Just because he doesn't teach it to this class doesn't mean that he doesn't know it. I see no error in this, he's just not providing a rigours proof as the work needed for this hasn't been taught to the students at this point.
@@tg509 I already mentioned that in his earlier video. Also, there are other ways to prove without using the series. He could use the proof that only requires precalculus. What he did here is incomplete with gaps that need to be proved. In mathematics, that is not acceptable. For example, Riemann hypothesis is not considered to be proved since we still have a gap that needs to be proved.
@@thomaskim5394 - This is highschool math. If he used the rigor you're demanding at this stage, everyone would be lost in the details. Besides, the statement you referenced is irrelevant to the lesson (at least up to this point).
for what value of k, the line 5x+ky+78=0 is tangent to the circle x^2+y^2= 36?
Can you help me with this question?
Hey there!
First of all, transform the equation of the tangent in explicit form. That would be: y=(-5/k)x-78/k. Therefore the coefficient (slope) m=-5/k, and n=-78/k.
Since this is a central equation of a circle, the centre has coordinates S(0,0) and the radius is 6.
The connection between these two is expressed with the formula (m*p-q+n)^2=r^2(m^2+1). Where as p and q are the coordinates of the centre of the circle - both 0. So if we use the numbers in the formula it be like this: (-5/k*0-0-78/k)^2=36(25/k^2+1).
Now you have an equation with 1 variable k.
I hope i helped, if you have any questions feel free to text me..
sin(x) = x
pi = 22/7, therefore, sin(pi) = 22/7 xDDDDDDD
You are using the sandwich or squeeze limit theorem without stating it.
When?