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The curve given by the polar equation r = a(1– cos ) is called a The cardioid has equation (22 + y? + ax)2 = a² (x? +y?) %3D To sketch the graph of r = 4(1 – cose) we first observe that if a point (r,0) lies on the graph then lies also on the same graph. This shows that the graph is symmetric about the |. If e is . Similarly, if 0 is Therefore, it suffices to let change between 0 and then r is 0. Next, we compute the values of r for increasing values of 0. If 0 is then r is approximately then r is Also if e is then r is approximately In the case of 8=Tt/2 we have r=4 because is zero. If 8 is we have r is Also, if 0=5Tt/6 then r is approximately Finally, r is when e is t. ja trom h m 0.54 2n/3 Cartesian у-ахis (r,-0) 6. 26 Tt/4 cosine T/3 cardioid the line y=x+2 Tt/6 1.17 7.46 х-ахis 2 8

The curve given by the polar equation r = a(1– cos ) is called a The cardioid has equation (22 + y? + ax)2 = a² (x? +y?) %3D To sketch the graph of r = 4(1 – cose) we first observe that if a point (r,0) lies on the graph then lies also on the same graph. This shows that the graph is symmetric about the |. If e is . Similarly, if 0 is Therefore, it suffices to let change between 0 and then r is 0. Next, we compute the values of r for increasing values of 0. If 0 is then r is approximately then r is Also if e is then r is approximately In the case of 8=Tt/2 we have r=4 because is zero. If 8 is we have r is Also, if 0=5Tt/6 then r is approximately Finally, r is when e is t. ja trom h m 0.54 2n/3 Cartesian у-ахis (r,-0) 6. 26 Tt/4 cosine T/3 cardioid the line y=x+2 Tt/6 1.17 7.46 х-ахis 2 8

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The curve given by the polar equation r = a(1 – cos ) is called a The cardioid has equation (22 + y? + ax)2 = a² (x? +y?) To sketch the graph of r = 4(1 – cose) we first observe that if a point (r,0) lies on the graph then lies also on the same graph. This shows that the graph is symmetric about the . If e is . Similarly, if 0 is Therefore, it suffices to let change between 0 and then r is 0. Next, we compute the values of r for increasing values of 0. If 0 is then r is approximately then r is Also if e is then r is approximately In the case of 8=T/2 we have r=4 because is zero. If 8 is we have r is Also, if 0=5Tt/6 then r is approximately Finally, r is when e is n. ja trom b h m 0.54 2/3 Cartesian y-axis (r,-0) 6. 26 Tt/4 cosine T/3 cardioid the line y=x+2 Tt/6 1.17 7.46 х-аxis 2 8
Transcribed Image Text:The curve given by the polar equation r = a(1 – cos ) is called a The cardioid has equation (22 + y? + ax)2 = a² (x? +y?) To sketch the graph of r = 4(1 – cose) we first observe that if a point (r,0) lies on the graph then lies also on the same graph. This shows that the graph is symmetric about the . If e is . Similarly, if 0 is Therefore, it suffices to let change between 0 and then r is 0. Next, we compute the values of r for increasing values of 0. If 0 is then r is approximately then r is Also if e is then r is approximately In the case of 8=T/2 we have r=4 because is zero. If 8 is we have r is Also, if 0=5Tt/6 then r is approximately Finally, r is when e is n. ja trom b h m 0.54 2/3 Cartesian y-axis (r,-0) 6. 26 Tt/4 cosine T/3 cardioid the line y=x+2 Tt/6 1.17 7.46 х-аxis 2 8
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