Please help me with these problems. Work and answer is appreciated! :) thanks.

1. Find on the interval theta is greater than or equal to 0 and less than 2pi; then find the general solution:

2.Find all solutions to 5cos(2pi x)=3 on the interval of x is greater or equal to 0 and less than or equal to 3.

3.Find # of solutions to cos(4x)=.724 on the interval of theta is greater or equal to 0 and less than 2pi

4.The angle of elevation from an airport to plane is 5 degrees. The altitude of the plane is 25000 ft. What is the distance from the plane to the airport?

5.A satellite launched into space reaches its farthest pt north of the equator 30 min after the launch. It reaches its farthest south of equator, distance of approx 2000 km, 90 min after that. If it takes the satellite 3 hours to orbit the earth, find an equation to model the satellites distance from the equator. (t=time)


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  1. It is not the function of this webpage to simply do the homework or assignments for students.
    It sure looks like that is what you want.

    These look like routine questions for a standard Calculus course.

    I will do #2 the way I would do it, follow this procedure to do the rest.

    5cos(2pi x)=3
    cos(2pi x)=3/5 = .6

    so the angle (2pi x) is either in quadrants I or IV according to the CAST rule

    set your calculator to radians

    then (2pi x) = .9273 OR (2pi x) = 2pi-.9273 = 5.358

    then x = .14758 or x = .8524

    Now the period of your original function is 2pi/2pi = 1

    so you can get addional answers by adding the period of 1 to any of your answers.
    So in the interval from 0 to 3
    x = .14758, 1.14758, 2.14758, .8524

    (I tested all of them, they work)

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  2. I don't get percentage.

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