On the same set of axes, sketch and label the graphs of the equations y = cos 2x and y = –2 sin x in the interval 0 ≤ x ≤ 2π. How many values of x in the interval 0 ≤ x ≤ 2π satisfy the equation –2 sin x – cos 2x = 3?

Question

On the same set of axes, sketch and label the graphs of the equations y = cos 2x and y = –2 sin x in the interval 0 ≤ x ≤ 2π.  How many values of x in the interval 0 ≤ x ≤ 2π satisfy the equation –2 sin x – cos 2x = 3?
 A.1
B.2
C.3
D.4
E.0

Steve · Answer

see the graphs here:

http://www.wolframalpha.com/input/?i=plot+y%3Dcos2x+and+y%3D-2sinx

However, it might be better to graph y = -cos2x, then the final graph would be easier to visualize:

http://www.wolframalpha.com/input/?i=plot+y%3D+-cos2x+and+y%3D-2sinx%2C+y+%3D+-cos2x-2sinx%2C+y%3D3

Anonymous · Answer

n b