Pre-Calculus Review 2

    This topic is a collection of problems and concepts that might help someone understand their working knowledge of Pre-Calculus 2.

Show all work and justify each step.

(1) Sketch the graphs of and on seperate axes. Label the period, phase shift, and amplitude. Also label any intercepts and asymptotes.

(2) Sketch the graphs of and on seperate axes. Label the period, phase shift, and amplitude. Also label any intercepts and asymptotes.

(3) Sketch the graphs of and on seperate axes. Label the period, phase shift, and amplitude. Also label any intercepts and asymptotes.

(4) Sketch the graphs of and on seperate axes. Label the period, phase shift, and amplitude. Also label any intercepts and asymptotes.

(5) Sketch the graphs of and on seperate axes. Label the period, phase shift, and amplitude. Also label any intercepts and asymptotes.


(6) Show the following are not identities:

    (a)
    
    (b)
    
    (c)
    
    (d)
    
(7) Show that the following are identities:

    (a)
    
    (b)
    
    (c)
    
    (d)
    
    (e)
    
(8) Show that if then and

(9) Find the solutions of the following equations that are in the interval [0,2 ).

    (a)
    
    (b)
    
    (c)
    
    (d)
    
    (e)

(10) Shown below is the graph of for Using calculus, it can be shown that the -coordinates of the turning points on the graph are solutions to the equation Determine the coordinates of these points.



(11) Find the exact value of and

(12) If and for a second quadrant angle and a third quadrant angle find
    (a)
    
    (b)
    
    (c)
    
    (d)
    
    (e)
    
    (f)
    
(13) If and are second quadrant angles such that and find

    (a)
    
    (b)
    
    (c) the quadrant containing

(14) Verify the following identities.

    (a)
    
    (b)
    
(15) Solve the following equations on the interval [0, ).

    (a)
    
    (b)
    
(16) Sketch the graph by expressing as a function involving only one trigonometric function. Label the amplitude, period, and phase shift.  

(17) Verify the identities:

    (a)
    
    (b)

    (c)

(18) Find all solutions to the equations that are in the interval [0, ).

    (a)
    
    (b)

(19) A graph of for is shown:



    (a) Find the
    
    (b) The -coordinates of the 13 turning points on the graph are solutions of Find these -coordinates.

(20) Solve given the following information.

    (a) and
    
    (b) and
    
    (c) and

(21) An airplane flies 165 miles from point in the direction and then travels in the direction for 80 miles. Approximate how far the airplane is from point

(22) Given a  rectangular box with dimensions Approximate the angle formed by a diagonal of the base and a diagonal of the wall.

(23) A baseball diamond has four bases (forming a square) that are 90 feet apart; the pitcher's mound is 60.5 feet from the home plate. Approximate the distance from the pitcher's mound to each of the other three bases.

(24) A rhombus has sides of length centimeters, and the angle at one of the vertices is Approximate the lengths of the diagonals.

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Cite this as:
Pre Calculus Two Review 2
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/pre-calculus-two-review-2.html