chaotic_butterflies
  • chaotic_butterflies
Trig help? How many radians on the unit circle would the minute hand travel from 0° if it were to move 5π inches? - more information below
Mathematics
jamiebookeater
  • jamiebookeater
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phi
  • phi
I would delete this part from your answer to Part 1 ***Using the information presented earlier, just multiply the 6 degrees by 25 minutes. 6*25 = 150, so the minute hand moves 150 radians from 1:25 to 1:50*** what you have below that line is correct: you get 6*25= 150 degrees and that is 5 pi/6 radians
phi
  • phi
For Part 2, this is muddled ***2pi(4)(5pi/6)/2pi = 10pi /3 inches**** you want arc= radius * angle(in radians) so just 4 * 5pi/6 = 10pi/3 inches (about 10.5 inches)
chaotic_butterflies
  • chaotic_butterflies
Oh, okay @Phi

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phi
  • phi
For the posted question **How many radians on the unit circle would the minute hand travel from 0° if it were to move 5π inches? ** use radius * angle = arc length they tell you radius is 4 they tell you arc length is 5 pi put those numbers into the formula what do you get ?
chaotic_butterflies
  • chaotic_butterflies
4*a = 5pi a = 5pi/4
phi
  • phi
yes, so the angle is 5 pi/4 radians (or 225 degrees) It will be halfway between 37 and 38 minutes past the hour
chaotic_butterflies
  • chaotic_butterflies
Awesome... so how do I find the coordinate point associated with that radian measure? I haven't even heard of finding something like that before .~.
phi
  • phi
exactly what is the question they asked?
chaotic_butterflies
  • chaotic_butterflies
Here's the whole thing: Part 1: How many radians does the minute hand move from 1:25 to 1:50? (Hint: Find the number of degrees per minute first.) Part 2: How far does the tip of the minute hand travel during that time? Part 3: How many radians on the unit circle would the minute hand travel from 0° if it were to move 5π inches? Part 4: What is the coordinate point associated with this radian measure?
phi
  • phi
I guess we put the origin at the center of the clock |dw:1434389528080:dw|
phi
  • phi
Either they want the (x,y) values of the tip of the minute hand or they want the (x,y) value on the unit circle (radius = 1). I'm not sure.
chaotic_butterflies
  • chaotic_butterflies
I looked this problem up on openstudy and someone else said the point was (-1,0) but there wasn't any actual explanation as to why...
phi
  • phi
(-1,0) looks strange. First, you would need the minute hand to be 5 inches (not 4 as you are using), and that would make 5*a= 5 pi, a=pi radians (not 5pi/4) or a= 180 degrees. Then they would say 180 degrees on the unit circle corresponds to point (-1,0) (notice in math we measure the angle counter-clockwise starting at the x-axis, and with a clock we measure clockwise (of course!) starting at the "y-axis".
phi
  • phi
The question posted here is not very clear, but because they are talking about a clock and a minute hand, my best guess is they want the (x,y) coords of the minute hand's tip... but who knows?? You could answer it 3 different ways and tell the teacher the question was very unclear, so you answered it 3 different ways
chaotic_butterflies
  • chaotic_butterflies
I'm not even quite sure how to find one of the ways... I mean I was confused about this teaching, but this is just absolutely foreign to me
phi
  • phi
do you know trig ?
chaotic_butterflies
  • chaotic_butterflies
I know bits and pieces, but by no means could I say that I've mastered it. I haven't had the best teaching, or any decent teaching on it for that matter... and to top it off, math has never been one of my strong points.
phi
  • phi
SOH CAH TOA when you have time, see https://www.khanacademy.org/math/geometry/right_triangles_topic/cc-geometry-trig/v/basic-trigonometry
phi
  • phi
If we interpret the question as asking for the coordinate point of 5pi/4 radians on the unit circle, we would do this |dw:1434390762967:dw| by coincidence we end up the same place. the answer would be x= r cos(225) y= r sin(225) but r is 1 for the unit circle, so you would get x= cos(225) = -cos(45) y= sin(225) = -sin(45) people memorize sin and cos of 45 degees. sin(45) = sqrt(2)/2 and cos(45) = sqrt(2)/2 (same thing)
phi
  • phi
so the answer is either \[ (-2 \sqrt{2}, -2 \sqrt{2} )\] for the minute hand which is 4 inches long or \[ \left(-\frac{\sqrt{2}}{2} , -\frac{\sqrt{2}}{2}\right) \] for the unit circle. notice the first answer is 4 times bigger than the second (because r=4 in the first case, and r=1 in the second case)
phi
  • phi
also, if you want more background, see https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func and make a point of watching the "Introduction to the unit circle" video.
chaotic_butterflies
  • chaotic_butterflies
thank you, I'll try to look at that! @Phi

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