Need some math help again

[imported_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 alot in advanced.

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

 

[Safeway]

You can do these...

#1: (1/6)*2*pi*3967
#2: I forgot
#3: Do it yourself

 

[eigen]

For number two imagine a plot of cos(x) now think on which of the restricted domains would it pass the horizontal line test.

 

[Nitemare]

1
D. None of the above 42 miles

2
E. None of the above 42 < x < 42

3
E. 42 degrees

 

[RichUK]

is the answer 5 :thumbsup:

 

[Toastedlightly]

for #1, imagine laying it out as a flat circle.

so r =3967 miles

make a 'cirlce' with that radius

the agle from the norht pole to the center of hte earth to houston is 60*

60* is 1/6th of a cirlce

so 1/6 * 2 * pi * 3967 = answer

 

[Toastedlightly]

for #2, you can't have 1/0. When does cosine = 0? Between the zeros of cosine is your answer

(-pi/2, pi/2)

edited for notation