{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW02-solutions

# HW02-solutions - qazi(kaq87 HW02 berg(55290 This print-out...

This preview shows pages 1–5. Sign up to view the full content.

qazi (kaq87) – HW02 – berg – (55290) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Locate the points given in polar coordinates by P parenleftBig 1 , 1 2 π parenrightBig Q parenleftBig 2 , 1 3 π parenrightBig , R parenleftBig 4 , 2 3 π parenrightBig , among 2 4 - 2 - 4 2 4 - 2 - 4 1. P : Q : R : 2. P : Q : R : 3. P : Q : R : correct 4. P : Q : R : 5. P : Q : R : 6. P : Q : R : Explanation: To convert from polar coordinates to Carte- sian coordinates we use x = r cos θ , y = r sin θ . For then the points P parenleftBig 1 , 1 2 π parenrightBig Q parenleftBig 2 , 1 3 π parenrightBig , R parenleftBig 4 , 2 3 π parenrightBig , correspond to P : Q : R : in Cartesian coordinates. keywords: polar coordinates, Cartesian coor- dinates, change of coordinates, 002 10.0points Find the Cartesian coordinates, ( a, b ), of the point given in polar coordinates by P (6 , π/ 3). 1. ( a, b ) = (6 , 6 3) 2. ( a, b ) = ( - 3 , 3 3) 3. ( a, b ) = ( - 6 , 3 3) 4. ( a, b ) = (3 , 3 3) correct 5. ( a, b ) = (3 3 , - 3) 6. ( a, b ) = (3 3 , 3) 7. ( a, b ) = (3 , - 6) 8. ( a, b ) = (6 3 , 6) Explanation: Since the relationship between Cartesian coordinates and polar coordinates is x = r cos θ , y = r sin θ , the point P (6 , π/ 3) is given in Cartesian co- ordinates by P (6 , π/ 3) = parenleftBig 6 cos π 3 , 6 sin π 3 parenrightBig = (3 , 3 3) . keywords: polar coordinates, Cartesian coor- dinates

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
qazi (kaq87) – HW02 – berg – (55290) 2 003 10.0points Find a polar equation for the curve given by the Cartesian equation y = 3 x 2 . 1. r = 3 csc θ tan θ 2. r = 3 sec θ tan θ 3. 3 r = sec θ cot θ 4. r = 3 csc θ cot θ 5. 3 r = sec θ tan θ correct 6. 3 r = csc θ cot θ Explanation: We have to substitute for x, y in y = 3 x 2 using the relations x = r cos θ , y = r sin θ . In this case the Cartesian equation becomes r sin θ = 3 r 2 cos 2 θ . Consequently, the polar form of the equation is 3 r = sec θ tan θ . 004 10.0points Which one of the following is the graph of the polar function r = 2 sin( θ/ 2) ? 1. 2. 3. correct 4. 5.
qazi (kaq87) – HW02 – berg – (55290) 3 6. Explanation: To determine the polar graph of r = 2 sin( θ/ 2) , look first at its Cartesian graph π 2 π 3 π 4 π 1 2 - 1 - 2 r θ Then, by tracing in polar coordinates the value of r as θ varies, looking especially at the values of θ where r = 0 and the values of r at θ = 0 , π , 2 π , 3 π , 4 π , we obtain the polar graph keywords: polar function, polar graph, sin function, cos function, 005 10.0points Which one of the following polar functions has graph 1. r = cos 2 θ 2. r = sin 2 θ 3. r = cos 4 θ 4. r = sin 3 θ correct 5. r = sin 4 θ 6. r = cos 3 θ Explanation: The graphs of r = sin θ , r = cos θ are circles passing through the origin. This question shows how the graphs change as the angle variable changes from θ to multiples 2 θ, 3 θ, etc . To determine the polar function look first at the Cartesian graph of the given trig func- tions: 1. r = sin 2 θ :

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
qazi (kaq87) – HW02 – berg – (55290) 4 r θ 1 2 1 - 1 2 - 1 π 2 π 2. r = sin 3 θ : r θ 1 2 1 - 1 2 - 1 π 2 π 3. r = sin 4 θ : r θ 1 2 1 - 1 2 - 1 π 2 π 4. r = cos 2 θ : r θ 1 2 1 - 1 2 - 1 π 2 π 5. r = cos 3 θ : r θ 1 2 1 - 1 2 - 1 π 2 π 6. r = cos 4 θ : r θ 1 2 1 - 1 2 - 1 π 2 π
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 16

HW02-solutions - qazi(kaq87 HW02 berg(55290 This print-out...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online