The point that is exactly halfway in between the two? What is this coordinate The distance, the line that connects them. Is exactly halfway between this point and that point? So this right here is kind of Try to figure out what is the coordinate of the point that We just drew a triangle thereĪnd realized that this was the hypotenuse. Wanted to figure out the distance between these Out that we could just use the Pythagorean theorem if we So that would be 1, 2,ģ, and then down 4. The difference between 3 and 5 is 2, so both numbers can be represented as 3 and (3+2), so in our previous way, we divided the distance by two and added it to the start point, and that's exactly what the formula does.we have added 3 and (3+2) together and divided by two, that is /2.notice that the difference between the numbers is getting divided by two and also 3 is repeated two times in the numerator!ģ comma negative 4. We know that point 4 is equidistant from both ends of the segment, but in general we can also find out the length of our segment and divide it by two to find the length between the median and each of the end points.our line segments length is 2 units, (since it starts at 3 and ends at 5) and if we wanted to find the midpoint of the segment, you can simply divide its length into halves and add the value to 3 (just try it on paper!) If we use the formula for median then its (3+5)/2, we also get 4, but why this works? Here's how it works Suppose you have a line segment on the number line with start point 3 and end point 5,the midpoint of the segment is 4. The formula for finding out the median is the sum of those two numbers divided by two. Since cos(2π + t) = cos(t) and sin(2π + t) = sin(t), the terminal point determined by 2π + t is (cos(t), sin(t)).Simply defined A median is a number that is between two numbers which is exactly halfway, like for example the median of 3 and 5 is 4 (There are many numbers between 3 and 5.but 4 is the median because the difference between 3 and 4 is the same as the difference between 4 and 5) So if you take on the number line, the median of 3 and 5 must be equidistant from both 3 and 5. Therefore, the terminal point determined by π + t is (-cos(t), sin(t)).ĭ) To find the terminal point determined by 2π + t, we substitute 2π + t into the coordinates of the terminal point. Using the angle addition formula, we have: Since cos(-t) = cos(t) and sin(-t) = -sin(t), the terminal point determined by -t is (cos(t), -sin(t)).Ĭ) To find the terminal point determined by π + t, we substitute π + t into the coordinates of the terminal point. Therefore, the terminal point determined by π - t is (-cos(t), -sin(t)).ī) To find the terminal point determined by -t, we substitute -t into the coordinates of the terminal point. Since cos(π) = -1 and sin(π) = 0, the expression simplifies to: Using the angle subtraction formula, we have: The terminal point determined by an angle t on the unit circle is given by (cos(t), sin(t)).Ī) To find the terminal point determined by π - t, we substitute π - t into the coordinates of the terminal point. To find the terminal point determined by each of the given angles, we can use the unit circle. It's like t saying, "I conquered the circle once, now let's do it again!" You go, t! In other words, it's a happy surprise!ĭ) 2Pi + t: Wow, t is really going for the record here! The terminal point determined by 2Pi + t is like t taking a victory lap around the unit circle. It's like finding money in your pocket you forgot about. It's like getting a bonus point on a test you thought you failed. The terminal point determined by Pi + t is like adding extra toppings to your pizza. So, it's like t got a bad haircut and is feeling a bit down, poor guy.Ĭ) Pi + t: Ah, the good old Pi and t combo. The terminal point determined by -t would be a reflection of t across the x-axis. So, the terminal point determined by Pi - t is probably (no pies left, because I ate them all, sorry).ī) -t: It seems like t is having a bit of a negative day here. A) Pi - t: Well, if Pi is the number of pies I've eaten, then Pi minus t would be the number of pies I have left.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |