I am a sub covering a Trig class, HELP!!! (please)?

Question

I am a substitute teacher, and I am covering a trig class on Friday. The teacher of this class is in the hospital and she didnt leave any work. I found the questions in a book, but there a no answers.

(1) Given the angle a and the radius r, to find the length of the subtending arc.
(a) a=0degrees 17 minutes, 48 seconds, r= 6.2935.

(b) a=121 degrees 6 minutes, 18 seconds, r= 0.2163

2.
Given the length of the arc L and the radius R, to find the angle subtended at the center.
(a) L=.16296, R=12.587.

(b) L=1.3672, R= 1.2978.

3.

Given the length of the arc L and the angle A which it subtends at the center, to find the radius.

(a) a= 0 degrees, 44 minutes, 30 seconds, L= .032592.

(b) a= 60 degrees, 21 minutes, 6 seconds, L=.4572.

4.A railroad curve forms a circular arc of 9 degrees, 36.7 minutes, the radius to the center line of the track being 2100 feet. If the gauge is 5 feet, find the difference in length of the two rails to the nearest half-inch.

Thank u

Answer 1

1.a). Convert the degree minutes and seconds to degrees.
0 degrees 17 min. 48 sec = 0.29666.. degrees.
Arc = 0.2966666/360 x 2 x pi x 6.2935
Arc = 0.3259 (4 dp)

1.b)
121 degrees 6 min 18 sec = 121.105 degrees
Arc = 121.105/360 x 2 x pi x 0.2163
Arc = 0.4572 (4 dp).

2.a).
L = x/360 x 2 x pi x R
x = (360 x L)/(2piR)
x = (360 x 0.16296)/(2 x pi x 12.587)
x = 0.741790754 degrees (0 degrees 44min 30.45 sec).

2.b).
Similarly
x = (360 x 1.3672)/(2 x pi x 1.2978)
x = 60.35967772 degrees ( 60 degrees 21 min 34.84 sec).

3.a).
0 degrees 44 min 30 sec = 0.74166666 degrees
R = (360 x L)/(2pia)
R = (360 x 0.032592)/(2 x pi x 0.74166666)
R = 2.51782 (5 dp)

3.b).
60 degrees 21 min 6 sec (60.35166666 degrees).
R = (360 x 0.4572)/(2 x pi x 60.351666666)
R = 0.43405 (5 dp)

4.
Outer rail (A) = a/360 x 2 x pi x R(larger radius)
Inner rail(A') = a/360 x 2 xpi x r (smaller radius)
Subtracting & factorising
A - A' = a/360 x 2 x pi x (R - r)
But R - r = 5 feet.
A - A' = a/360 x 2 x pi x 5
& a = 9 degrees 36.7 mins = 9.61166666 degrees.
A - A' = 9.61166666/360 x 2 x pi x 5
A - A' = 0.838776149.ft
(A - A') x 12 = 0.838776149 x 12 = 10.0653 ins.
A - A' = 10 ins ( to nearest 1/2 inch)

Answer 2

I’ll answer first two. But double check these answers. Th rest should be easy. Good luck!

(1)

First convert angle a into decimal degrees. 60 minute =1 degree, and 3600 seconds = 1 degree.

So for (a), since a = 0degrees 17 minutes, 48 seconds,
a = 17/60 + 48/3600 = (60*17 +48)/3600 = 1068/3600

Now apply formula = (a/360)(2pi*r)

Arclength = (1068/3600)(1/360)(2pi)(6.2935) = approx. 0.0326

Similarly for (b),

Arclength = (121.105/360)(2pi)(0.2163) = approx. 0.4572

(2)

Given the length of the arc L and the radius R, to find the angle subtended at the center.

(a) L= .16296, R=12.587.

Use the formula L = (angle in radians)(R)

So Angle = L/R (in radians)

Angle = .16296/12.587 = 0.013 rad

You may convert this to degrees by multiplying 180/pi

Answer in degrees: (0.013)(180/pi) = 0.742 degrees

(b) L=1.3672, R= 1.2978.

Similarly, Angle = 1.3672/1.2978 = 1.053 (or 60.36 degrees)

Also you can break these answers further down to minutes and seconds.

(3)

First convert all to degrees then to radians. Finally apply, L = (Angle)R To find R.

(4) Apply same concepts and formula from above.

Answer 3

Ask the class to make a plot of the values they get for the homework. The one with the most will probably be the answer. But if in doubt, ask another Trig teacher.

Answer 4

Is there another trig teacher at that school? If not find another math teacher and get some sort of review work for them to do at least for that one day. If you are not familiar with the material, even with the answers it may be frustrating for the students as well as for you.

Answer 5

You're fired.

right, the teacher's text book has no answers, lmao.

Answer 6

hmmmmm sounds to me like you're a student trying to get the answers!!! maybe ask your "students" the questions and see what they come up with! and then MAJORITY wins!