Let f(x, y) = sin(x y − x − 3y+3). (i) Determine the domain and range of f. (ii) Factor the argument of the sin function. Does this factored form give any hints about the appea ance of the surface z = f(x, y)? (iii) Find a relationship for the x cross-sections by letting x = k, k = R. Then, • tabulate the relationships for k = 0, 1, . . ., 6; • sketch the relationships for k = 3, 4, 5, 6 on the interval y € [1 − π, 1±Ã] ; and ⚫ with respect to the cross-sections for k = 4, 5, 6, describe the cross-sections for k = 0, 1, 2.
Let f(x, y) = sin(x y − x − 3y+3). (i) Determine the domain and range of f. (ii) Factor the argument of the sin function. Does this factored form give any hints about the appea ance of the surface z = f(x, y)? (iii) Find a relationship for the x cross-sections by letting x = k, k = R. Then, • tabulate the relationships for k = 0, 1, . . ., 6; • sketch the relationships for k = 3, 4, 5, 6 on the interval y € [1 − π, 1±Ã] ; and ⚫ with respect to the cross-sections for k = 4, 5, 6, describe the cross-sections for k = 0, 1, 2.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
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Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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![Let f(x, y) = sin(xy-x-3y+3).
(i) Determine the domain and range of f.
(ii) Factor the argument of the sin function. Does this factored form give any hints about the appear-
ance of the surface z = = f(x, y)?
(iii) Find a relationship for the x cross-sections by letting x = k, k = R. Then,
⚫ tabulate the relationships for k = 0, 1, ..., 6;
-
• sketch the relationships for k = 3, 4, 5, 6 on the interval y € [1 − π, 1 + π] ; and
⚫ with respect to the cross-sections for k = 4, 5, 6, describe the cross-sections for k = 0, 1, 2.
(iv) Find a relationship for the level curves / contours by letting z = m, m Є R. You must recognise
the periodic nature of f and ensure the relationship accounts for it.
(v) Sketch the contours m = 0 on the interval x € [−1,7], y ≥ [−3, 5] .
Ꮖ
(vi) Which of the surfaces below is a graph of this function?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1750264-b177-480f-8500-2593618fe8d1%2F96719652-5483-497b-8b81-ac6affc7e2ed%2F9hzfzi6_processed.png&w=3840&q=75)
Transcribed Image Text:Let f(x, y) = sin(xy-x-3y+3).
(i) Determine the domain and range of f.
(ii) Factor the argument of the sin function. Does this factored form give any hints about the appear-
ance of the surface z = = f(x, y)?
(iii) Find a relationship for the x cross-sections by letting x = k, k = R. Then,
⚫ tabulate the relationships for k = 0, 1, ..., 6;
-
• sketch the relationships for k = 3, 4, 5, 6 on the interval y € [1 − π, 1 + π] ; and
⚫ with respect to the cross-sections for k = 4, 5, 6, describe the cross-sections for k = 0, 1, 2.
(iv) Find a relationship for the level curves / contours by letting z = m, m Є R. You must recognise
the periodic nature of f and ensure the relationship accounts for it.
(v) Sketch the contours m = 0 on the interval x € [−1,7], y ≥ [−3, 5] .
Ꮖ
(vi) Which of the surfaces below is a graph of this function?
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