Name_________________________________
Graphing Systems of Trig Equations
Date______
10H Per___
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Ex. 1: During an aerial show, the Red Barron’s plane is flying a course represented by the equation y   cos( x) , while
Amelia Earhart is flying along a path represented by y  2 sin x .
a) On the accompanying grid, sketch both paths over the interval 0  x  2 .
b) How many times do the paths of the pilots intersect over the interval?
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Ex. 2: The flight of hawk is modeled by the equation y  2 sin( x)  1 , while the path of its prey is moving according the
equation y  cos 2 x . Graph their paths to determine how many times, over the course of 0  x  2 , the hawk will have
the opportunity to catch its prey.
Homework:
1. a) On the same set of axes, sketch and label the graphs of the equations y = sinx and y = 2cos2x
over    x   .
b) How many solutions are there to the equation sinx – 2cos2x = 0 over the interval 0  x   ?
2. Graph y = 2sinx – 3 over 0 ≤ x ≤ 2π
3. If sin  
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and sec  0 , what is the exact value of cot  ?
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4. Express cos97o as the function value of an acute angle that is less than 45o.
5. What is the exact value of csc225o?
6. a) On the same set of axes, sketch and label the graphs of the equations y = -2cosx + 1 and y = 2sin2x
over 0  x  2
b) How many solutions are there to the equation -2cosx + 1 = 2sin2x over the interval 0  x   ?