degrees of latitude / area of slice of pizza / angular veloc

[Misslovey23]

I am taking trigonometry in college, and I'm having trouble with a few exercises:

1) A plane travels 1200 miles south. How many degrees of latitude is this?

2) How fast is the outer edge of a 12-inch diameter record moving if the record turns at 33 1/3 rpm?

3) A wheel turns at 10 rpm. The outer edge moves at 20 ft/sec. What is the radius?

4) You are sharing an 18 inch pizza (that is, a pizza with a 9-inch radius). You get a 35 degree slice. What is your area?

5) Velocity: 60mph; angular velocity: 5rad/hour. What is the radius?

I hope somebody can please help me, it would really mean alot =)
Thanks!!

 

[stapel]

1) What is the circumference of the earth? How many degrees of latitude are between the two poles? So how many miles are in each degree? So how many degrees correspond to 1200 miles?

2) What is the radius of the disc? What then is the circumference? If the disc rotates 33¹/₃ times in one minute (that is, if a point on the circumference orbits the center this many times), how far has the outer edge (that point) travelled in the minute?

3) If the wheel turns ten times in a minute, how far around does it get in one second? That is, how much of a rotation is accomplished in one second? If the arc-length is 20 feet per second, then, given the angle (portion of a rotation of 360°) that you just calculated, what is the radius?

4) What is the area of a sector with radius r = 9 and angle-measure 35°?

5) The speed of a point on the edge is 60 miles per hour. The object is rotating at five radians per hour (where 2pi radians is "once around"). So, given an arc length of 60 miles and an angle measure of five radians, what is the radius?

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[Misslovey23]

Thank you so much Im gonna work on them and reply if i need some more help.
Your awesome!!