RANSCIRBE THE FOLLOWING SOLUTION IN DIGITAL FOR
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 79E
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Question
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TRANSCIRBE THE FOLLOWING SOLUTION IN DIGITAL FORMAT
![2
Giren function is, x²y² where, x=6cost,
y=6Sint
0≤t≤2π
x²y² = 36 cos²4 - 6-sin't Also, dx=-6sintat
= 36 [Cos²t -sin²t]
dy=6costat
= 36 Cosat.
27
& (x²=y²) dx = √ [36 Cos2+] [-6sint]dt
O
-
= -108
=
211
36 (-6) [Cos2tsint]dt
271
(36x66)) [Sin(2t+t)-sin(2t-t)
2
(Using 2 cosAsinB =
211
⇒ (36 (-3) (sin 3t-sint) dt
271
211
Sin3t + 108 sint dt =
= 36 (1-01) - 108 (1-1)
= 0
dt
sin (A+B). -
Sin(A-B)
1271
+401038/ 2013 1
Cos
-108 [cost]27
NOW,
271
$(x²y²2)dy = √36cos2+ x 6 cost dt
271
= 36x6 ²7 [Cos(3+) + Cost] dt
2
(since 2cosA COSB-Cos(A+B) + Cos(A-B)
=108
=108
³ [0 +0]
=0.
= 0
sin3t + Sint
3
= 36.6
Now, $1x²y³ds, ds= √√36sin't +36 cos²4 dt
ds = 6dt
271
⇒ f (x²=y³ds = √36 cos2t-6 dt
127 Claszt dt
= 36×6
=
277
sint 12¹
(0)
2
(ds = √√ (da) ² (dy) ²
dt
Sinet 7217
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71a8087c-0454-49ea-8aab-efcec8f7f928%2F4b0694fe-86cd-48c6-bdc9-5247210c3252%2Fv94tct_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2
Giren function is, x²y² where, x=6cost,
y=6Sint
0≤t≤2π
x²y² = 36 cos²4 - 6-sin't Also, dx=-6sintat
= 36 [Cos²t -sin²t]
dy=6costat
= 36 Cosat.
27
& (x²=y²) dx = √ [36 Cos2+] [-6sint]dt
O
-
= -108
=
211
36 (-6) [Cos2tsint]dt
271
(36x66)) [Sin(2t+t)-sin(2t-t)
2
(Using 2 cosAsinB =
211
⇒ (36 (-3) (sin 3t-sint) dt
271
211
Sin3t + 108 sint dt =
= 36 (1-01) - 108 (1-1)
= 0
dt
sin (A+B). -
Sin(A-B)
1271
+401038/ 2013 1
Cos
-108 [cost]27
NOW,
271
$(x²y²2)dy = √36cos2+ x 6 cost dt
271
= 36x6 ²7 [Cos(3+) + Cost] dt
2
(since 2cosA COSB-Cos(A+B) + Cos(A-B)
=108
=108
³ [0 +0]
=0.
= 0
sin3t + Sint
3
= 36.6
Now, $1x²y³ds, ds= √√36sin't +36 cos²4 dt
ds = 6dt
271
⇒ f (x²=y³ds = √36 cos2t-6 dt
127 Claszt dt
= 36×6
=
277
sint 12¹
(0)
2
(ds = √√ (da) ² (dy) ²
dt
Sinet 7217
2
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