## chaotic_butterflies one year ago 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

1. 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

2. 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)

3. chaotic_butterflies

Oh, okay @Phi

4. 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 ?

5. chaotic_butterflies

4*a = 5pi a = 5pi/4

6. 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

7. 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 .~.

8. phi

exactly what is the question they asked?

9. 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?

10. phi

I guess we put the origin at the center of the clock |dw:1434389528080:dw|

11. 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.

12. 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...

13. 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".

14. 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

15. 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

16. phi

do you know trig ?

17. 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.

18. phi

SOH CAH TOA when you have time, see https://www.khanacademy.org/math/geometry/right_triangles_topic/cc-geometry-trig/v/basic-trigonometry

19. 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)

20. 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)

21. 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.

22. chaotic_butterflies

thank you, I'll try to look at that! @Phi