Radians, sine, cos, tan, and angular distance

[spardawg]

1) Consider an angle that intercepts an arc of length 80 meters. If the arc is on a circle with radius 8m, what is the measure of the angle in degrees?
-I have the measure of the angle in radians already by dividing 80 by 8, but I don't know how to get the degrees of the angle.

2) A point on a doorknob moves 20 inches. If the knob has a radius of 8 inches, how many degrees did the point turn?
-I don't have much on this one, but do have that you might have to find the arc length and then set up a porportion?

3)What is the anular distance traveled by a racecar averaging 190mph in the Indy 500?
-All I have so far for this one is the beginning of the porportion 190mi over 1 hour...

4)Without a calculator, find the sine, cosine, and tangent of 3/4pi and 70pi.
-I know you have to find the coordinates of the point on the circle because you could then plug in the x and y to the ratios of sine cosine and tangent, but I don't have the radius....?

5) A truck with a tire of radius 18 inches is traveling at 45mph. What is the angular speed of a point on the tire in radians per second?
-I have already that there is definitely going to be porportion...Thank you muy muchoo!!!!

 

[Deleted member 4993]

1) Consider an angle that intercepts an arc of length 80 meters. If the arc is on a circle with radius 8m, what is the measure of the angle in degrees?
-I have the measure of the angle in radians already by dividing 80 by 8, but I don't know how to get the degrees of the angle.

A full circle will have an arc length of (8*2*? = ) ~49 meters - are you sure you are reading the problem correctly?

2) A point on a doorknob moves 20 inches. If the knob has a radius of 8 inches ( that's a huge door knob), how many degrees did the point turn?
-I don't have much on this one, but do have that you might have to find the arc length and then set up a porportion?

3)What is the anular distance traveled by a racecar averaging 190mph in the Indy 500?
-All I have so far for this one is the beginning of the porportion 190mi over 1 hour...

4)Without a calculator, find the sine, cosine, and tangent of 3/4pi and 70pi.
-I know you have to find the coordinates of the point on the circle because you could then plug in the x and y to the ratios of sine cosine and tangent, but I don't have the radius....?

5) A truck with a tire of radius 18 inches is traveling at 45mph. What is the angular speed of a point on the tire in radians per second?
-I have already that there is definitely going to be porportion

\(\displaystyle v = r * \omega\)

...Thank you muy muchoo!!!!

 

[spardawg]

On question 1, it asks for the measure of the angle in radians too. That was part one. Otherwise, that is the correct problem. Also, what does v=r*w mean??

 

[Deleted member 4993]

On question 1, it asks for the measure of the angle in radians too. That was part one. Otherwise, that is the correct problem.

In that case - I am confused about the problem.

Also, what does v=r*w mean??

In curvelinear motion:

\(\displaystyle v \ = \ linear \ speed\)

\(\displaystyle \omega \ = \ angular \ speed\)

\(\displaystyle r \ = \ radius \\)