4. Graphing Trigonometric Functions
Graphs of Tangent and Cotangent Functions
4. Graphing Trigonometric Functions
Graphs of Tangent and Cotangent Functions - Video Tutorials & Practice Problems
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concept
Introduction to Tangent Graph
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5mPlay a video:
2
Problem
ProblemBelow is a graph of the function y=tan(bx). Determine the value of b.
A
b=41
B
b=π
C
b=2
D
b=21
3
example
Example 1
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4
concept
Introduction to Cotangent Graph
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5mPlay a video:
5
Problem
ProblemBelow is a graph of the function y=cot(bx+2π). Determine the value of b.
A
b=41
B
b=1
C
b=2
D
b=21
6
example
Example 1
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3mPlay a video:
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PRACTICE PROBLEMS AND ACTIVITIES (59)
- Graph each function over a one-period interval.y = 3 sec [(1/4)x]
- Concept Check Match each function with its graph in choices A–F.7. 8.9.10. 11. y = cot (x + π ) ...
- Graph each function over a one-period interval.y = - (1/2) csc (x + π/2)
- Graph each function over a one-period interval. See Examples 1–3.y = tan 4x
- For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = (1/2)...
- For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = 2 sec(...
- Graph each function over a one-period interval.y = csc (x - π/4)
- Graph each function over a one-period interval. See Examples 1–3.y = 2 tan x
- For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = 1/3 ...
- For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = cot (x...
- Graph each function over a one-period interval.y = sec (x + π/4)
- Graph each function over a one-period interval.y = 2 tan (¼ x)
- Graph each function over a one-period interval.y = csc((1/2)x - π/4)
- Graph each function over a one-period interval.y = cot (3x)
- Graph each function over a one-period interval.y = (1/2) csc (2x + π/2)
- Graph each function over a one-period interval.y = -2 tan (¼ x)
- Identify the circular function that satisfies each description.period is π; function is decreasing on the int...
- Match each function in Column I with the appropriate description in Column II.Iy = -4 sin(3x - 2)IIA. amplitud...
- Graph each function over a one-period interval.y = 2 + 3 sec (2x - π)
- Graph each function over a one-period interval.y = ½ cot (4x)
- Graph each function over a one-period interval.y = ½ sec x
- Graph each function over a one-period interval.y = 1 - (1/2) csc (x - 3π/4)
- Graph each function over a two-period interval.y = tan(2x - π)
- Determine an equation for each graph.
- Graph each function over a two-period interval.y = cot (3x + π/4)
- Graph each function over a one-period interval.y = -1 + csc x
- Determine an equation for each graph.
- Graph each function over a two-period interval.y = 1 + tan x
- Determine an equation for each graph.
- Graph each function over a two-period interval.y = 1 - cot x
- Decide whether each statement is true or false. If false, explain why.The tangent and secant functions are und...
- Graph each function over a two-period interval.y = -1 + 2 tan x
- Decide whether each statement is true or false. If false, explain why.The graph of y = sec x in Figure 37 sugg...
- Graph each function over a two-period interval.y= -1 + (1/2) cot (2x - 3π)
- Graph each function over a two-period interval.y = 1 - 2 cot [2(x + π/2)]
- Consider the function g(x) = -2 csc (4x + π). What is the domain of g? What is its range?
- Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midp...
- Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midp...
- A rotating beacon is located at point A, 4 m from a wall. The distance a is given bya = 4 |sec 2πt|,where t is...
- Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midp...
- Consider the following function from Example 5. Work these exercises in order.y = -2 - cot (x - π/4)Based on t...
- For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.y = tan 3x
- Consider the following function from Example 5. Work these exercises in order.y = -2 - cot (x - π/4)Use the fa...
- Fill in the blank(s) to correctly complete each sentence.The graph of y = 3 + 5 cos (x + π/5) is obtained by s...
- Match each function with its graph in choices A - D.y = sec (x - π/2)
- Match each function with its graph in choices A–F.y = tan (x - π )A. <IMAGE> B. <IMAGE> C. <IMA...
- In Exercises 25–28, use each graph to obtain the graph of the corresponding reciprocal function, cosecant or s...
- In Exercises 25–28, use each graph to obtain the graph of the corresponding reciprocal function, cosecant or s...
- In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 3 csc x
- In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 1/2 csc x/2
- In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 2 sec x
- In Exercises 29–44, graph two periods of the given cosecant or secant function. y = sec x/3
- In Exercises 29–44, graph two periods of the given cosecant or secant function. y = −2 csc πx
- In Exercises 29–44, graph two periods of the given cosecant or secant function. y = −1/2 sec πx
- In Exercises 29–44, graph two periods of the given cosecant or secant function. y = csc(x − π)
- In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 2 sec(x + π)
- In Exercises 45–52, graph two periods of each function. y = sec(2x + π/2) − 1
- In Exercises 45–52, graph two periods of each function. y = csc|x|
- In Exercises 53–54, let f(x) = 2 sec x, g(x) = −2 tan x, and h(x) = 2x − π/2. Graph two periods of y = (f∘h)(...