I with 3 precalculus problems.

[takuma]

Hello everyone I am homeschooling and I am stuck on 3 of my precalculus problems. If anyone could help me out that would be great.

1. The latitude of Houston, Texas is about 30° N. About how far is it from the North Pole given the radius of the Earth is 3967 miles?

a. 23,778 miles
b. 4150 miles
c. 2075 miles
d. none of the above

2. With what restricted domain would the cosine function have an inverse?

a.{x| 0 <= x <= pi}
b.{x| -pi/2 <= x <= pi/2}
c.{x| -pi/2 < x < pi/2}
d.{x| 0 < x < pi}


3. Find the direction of angle alpha(The greek 'a' thing) for whose equation is x^2 - 2xy + 2y^2 = -4.

a. .55
b. pi/8
c. 1.1
d. pi/3


I was able to do all the other problems but these ones for some reason I just got stuck on. I would like to say thanks a lot in advanced.

Edit: I forgot to say if you could explain how you got the answer and stuff that would be the most helpful.

 

[NewScientist]

Takuma, it is always ncie if you can tell us how far you have got yourself so we can help you rather do it for you! So if you would be so kind as to show some working I'm sure we can get some good input going!

-NewScientist

 

[takuma]

Well to be honest i didnt get anywhere. lol I just didnt know where to start. There are no examples like these in the book.

 

[NewScientist]

Okay, well I'll give you tips,

No.1 - the question is not specific to houston as you no doubt rationalised.
Now there are two questions they may be asking. One, it may be the straight line distance from the top of the circle (treating the Earth as a cirlce as you have been given a radius) to a point 30 degrees round so it is just a traingle in a segment question - the equations for which are well known.
Or it may be asking for you to find the distance if you follow the curviture of the Earth, this is still easy as you are dealing with a segment once more. The idea of the Earth is just to through you off - treat it like a circle!

For question 2 remember that for a function to have an inverse, it must be one-to-one. This means that each x must have one and only one y and each y must have one and only one x.

For 3, think about graphs.

-NewScientist