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Find the points at which the following polar curve has a horizontal or a vertical tangent line. r= 9 sin 20 dy Find as a function of 0. dx

Find the points at which the following polar curve has a horizontal or a vertical tangent line. r= 9 sin 20 dy Find as a function of 0. dx

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 13E
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Find the points at which the following polar curve has a horizontal or a vertical tangent line. r= 9 sin 20 dy Find as a function of 0. dx dy %D dx At what points does the polar curve have a horizontal tangent line? O A. 0. (0.). (29,7+0,), where tan 0, = /2 (*9,0,), and where tan 0, = v2 9,л + 3 (0.). (0). (+6VZ.0,)., and (26/2,x- ,). where tan 0, = 1 O B. = - Oc. (0,0) (0,7). c. (0,0), (0,1), ( ±6/2,0,), and ( +6/2,1 -0,), where tan 0, D. (0,0), (0,71), ( ± 6/3,0,), and (+ 6V3 ,-0,), where tan 0, V3 = At what points does the polar curve have a vertical tangent line? 3n 1 0.5. (0.. (*6/3,02), and (+6V3,7-0,2), where tan 0, = - V3 O B. (0,0), (0,71), (±6/2,02), and ( ±6V2,1 - 02), where tan 02 = /2 1 Oc. (0,0), (0,1), (±9,02), and (+9,7 +02), where tan 0, = 12 1 O D. 0.5). (0.. = (26/2,02), and (+6VZ,r- 02), where tan 0,
Transcribed Image Text:Find the points at which the following polar curve has a horizontal or a vertical tangent line. r= 9 sin 20 dy Find as a function of 0. dx dy %D dx At what points does the polar curve have a horizontal tangent line? O A. 0. (0.). (29,7+0,), where tan 0, = /2 (*9,0,), and where tan 0, = v2 9,л + 3 (0.). (0). (+6VZ.0,)., and (26/2,x- ,). where tan 0, = 1 O B. = - Oc. (0,0) (0,7). c. (0,0), (0,1), ( ±6/2,0,), and ( +6/2,1 -0,), where tan 0, D. (0,0), (0,71), ( ± 6/3,0,), and (+ 6V3 ,-0,), where tan 0, V3 = At what points does the polar curve have a vertical tangent line? 3n 1 0.5. (0.. (*6/3,02), and (+6V3,7-0,2), where tan 0, = - V3 O B. (0,0), (0,71), (±6/2,02), and ( ±6V2,1 - 02), where tan 02 = /2 1 Oc. (0,0), (0,1), (±9,02), and (+9,7 +02), where tan 0, = 12 1 O D. 0.5). (0.. = (26/2,02), and (+6VZ,r- 02), where tan 0,
Find the points at which the following polar curve has a vertical or a horizontal tangent line. r= 2 cos 0 dy Find as a function of 0. dx dy %3D dx At what points does the polar curve have a vertical tangent line? O A. The polar curve has a vertical tangent line at (2,0) and 0, (). (v2. and (- v2. (2) 21 B. The polar curve has a vertical tangent line at (2,0), 1, and C. The polar curve has a vertical tangent line at V2,- 4 4 () D. The polar curve has a vertical tangent line at 2, and 2, At what points does the polar curve have a horizontal tangent line? (0) IT A. The polar curve has a horizontal tangent line at (2,0) and B. The polar curve has a horizontal tangent line at V2, and 4 O C. The polar curve has a horizontal tangent line at 2, and |2, 6. 3 D. The polar curve has a horizontal tangent line at (2,0), 1, and 3
Transcribed Image Text:Find the points at which the following polar curve has a vertical or a horizontal tangent line. r= 2 cos 0 dy Find as a function of 0. dx dy %3D dx At what points does the polar curve have a vertical tangent line? O A. The polar curve has a vertical tangent line at (2,0) and 0, (). (v2. and (- v2. (2) 21 B. The polar curve has a vertical tangent line at (2,0), 1, and C. The polar curve has a vertical tangent line at V2,- 4 4 () D. The polar curve has a vertical tangent line at 2, and 2, At what points does the polar curve have a horizontal tangent line? (0) IT A. The polar curve has a horizontal tangent line at (2,0) and B. The polar curve has a horizontal tangent line at V2, and 4 O C. The polar curve has a horizontal tangent line at 2, and |2, 6. 3 D. The polar curve has a horizontal tangent line at (2,0), 1, and 3
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