Question

1. Complete the tables of values below for graphing the secant and cotangent functions. You can type “U” for an undefined value. Use exact values with fractions and square roots, not the decimal approximations. For example, use 3/2 rather than 0.866 (pictures attached)
2. Graph the secant graph for 0 ≤ x ≤ 2π. Graph the cotangent graph for 0 ≤ x ≤ 2π. (don't need these pictures I have them)


3. Indicate whether each of the three reciprocal functions (cosecant, secant, and cotangent) is a periodic function. If so, state the period of each.


4. List the domain and range for the secant and cotangent functions. (Use "pi" for π.)


5. Compare the graphs of the cosecant and secant functions. How are they different? How are they similar?

Answer 1

Step-by-step explanation:

1. All the trigonometric values can be found using the unit circle.  See attached table.

2. Graph:

desmos.com/calculator/10n7yrm3tm

3. All trig functions are periodic functions.  The period of secant and cosecant is 2π.  The period of cotangent is π.

4. Using the table from step 1 and the graph from step 2, secant has a domain of x ≠ pi/2, 3pi/2 and a range of x ≤ -1, x ≥ 1.  Cotangent has a domain of x ≠ 0, pi, 2pi and a range of -∞ < x < ∞.

5. Graph:

desmos.com/calculator/tldiqt7qra

Cosecant has the same graph as secant shifted π/2 to the right.  So they have different domains, but the same range.