Draw the graph of f(x) = tan x and g(x) = 2cos x for 180 _< thetha _< 180
{since its a graph I'm sure how to draw it here}
you cannot draw it here. However, you can see them here:
http://www.wolframalpha.com/input/?i=plot+y%3Dtan%28x%29%2C+y%3D2cos%28x%29+for+x+%3D+-pi..pi
x is in radians, but the graphs look the same for degrees:
http://www.wolframalpha.com/input/?i=plot+y%3Dtan%28x*pi%2F180%29%2C+y%3D2cos%28x*pi%2F180%29+for+x+%3D+-180+..+180
To graph the functions f(x) = tan(x) and g(x) = 2cos(x) for the given range of 180 ≤ θ ≤ 180°, we can follow these steps:
1. Determine the intervals where the functions are defined:
- For f(x) = tan(x), the function is defined for all real numbers x except x = (2n + 1)π/2, where n is an integer. However, in the given range, tan(x) is not defined for any value of x.
- For g(x) = 2cos(x), the function is defined for all real numbers x.
2. Plotting the graph:
Since f(x) = tan(x) is not defined in the given range, we do not draw the graph for f(x).
For g(x) = 2cos(x), we can proceed as follows:
a. Set up the coordinate system with the x-axis and y-axis intersecting at the origin.
b. Mark the key points on the graph:
- To find the key points, we need to consider the interval 180 ≤ θ ≤ 180°, which is just a single point on the unit circle, namely (0, -1).
c. Draw the cosine graph passing through the key points:
- The cosine function starts at (0, 1), reaches a minimum at (-π, -1), goes back to a maximum at (0, 1), and repeats this pattern.
- Since the given range is only a single point, we only plot (0, -1) on the graph.
d. Scale the axes appropriately, keeping in mind the range of values.
e. Draw the graph of g(x) = 2cos(x), passing through the point (0, -1).
Please note that the given range of 180 ≤ θ ≤ 180° is a single value and does not allow the functions to show any variation or behavior.