Unit 5B: TASK 4: Graphing Reciprocal (or “Co”) Trigonometric Functions
Name: ___________________________________________
Date: ________________
Period: _____
I. COTANGENT
1. The cotangent is the reciprocal of the tangent. So cotangent θ =
=
a.) Using this definition, complete the chart below.
x
-π
π
0
Cotangent
x
b.) graph the cotangent on the given grid.
2.) Use your graph and chart to answer the following questions.
a. What is the period of y = cot x? __________________
b. What is the domain and range of y = cot x? Domain: ____________ Range: ____________
c. What is the y-intercept of y = cot x? __________________
d. Where do the x-intercepts occur in y = cot x? __________________
e. Does the graph have any maximum or minimum values?
_______ If so, what are they? __________
f. Does the graph have any asymptotes? ______ If so, where are they? ___________________________
2. Use your graph to find the following values of cotangent.
a. cot(-5π)=
b. Cot
=
c.
Cot
=
d.
cot(0)=
II. COSECANT & SECANT
The cosecant and secant functions are reciprocals of the sine and cosine functions. The cosecant, csc, is
the reciprocal of the sine function. The secant, sec, function is the reciprocal of the cosine function.
csc =
sec θ =
**These graphs will be explored using a graphing calculator.**
1. Graph the sine and cosecant function on the same set of axis.
Enter the sine function in y1.
Check your window and mode to make sure there are at least two periods of the graph on your screenone in the 1st quadrant and one in the 2nd quadrant.
Enter the cosecant function in y2.
The cosecant function may need to be entered as
.
a. What are the values of sin x at x = -2π, - π, 0, π, and 2π? ________________________
b. What are the values of csc x at x = -2π, - π, 0, π, and 2π? ____________ Why? ___________________
c. What are the values of x where the graphs are tangent? _______________________________________
Answer the following questions for csc x.
d. What is the period? ____________
g. What is the domain and range? Domain: ____________ Range: ____________
h. What is the y-intercept? ____________
i. Where do the x-intercepts occur? ____________
a. Does the graph have any maximum or minimum values? ______ If so, what are they? ____________
b. Does the graph have any asymptotes? ______ If so, where are they? ____________________________
2. Graph the cosine and secant function on the same set of axis.
Enter the cosine function in y1.
Check your window and mode to make sure there are at least two periods of the graph on your screenone in the 1st quadrant and one in the 2nd quadrant.
Enter the secant function in y2.
The secant function may need to be entered as
.
a. What are the values of cos x at x = -3π/2, - π/2, π/2, and 3π/2? __________________
b. What are the values of sec x at x = x = -3π/2, - π/2, π/2, and 3π/2? ____________ Why? ____________
c. What are the values of x where the graphs are tangent? _______________________________________
Answer the following questions for sec x.
e. What is the period? ____________
j. What is the domain and range? Domain: ____________ Range: ____________
k. What is the y-intercept? ____________
l. Where do the x-intercepts occur? __________________
c. Does the graph have any maximum or minimum values? ______ If so, what are they? ______________
d. Does the graph have any asymptotes? ___________ If so, where are they? _______________________
III. ALL 6 TRIGONOMETRIC FUNCTIONS: Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent
3. Which of the 6 trig functions have periods of 2π? __________________________________________
4. Which of the 6 trig functions have periods of π? ____________________________________________