8.5+OFSA

OFSA for Polar Graphs

This page contains peer generated questions that help you assess your understanding. Remember that questions may not represent the rigor of the questions you may be expected to complete on formal assessments. This page is simply an OFSA - opportunity for self assessment.


 * Question 1**

math \text{Graph the equation} \; r=1-6\cos\theta\\ \\

\text{A. \indent}\\ math

math \text{B. \indent}\\ math



math \text{C. \indent}\\ math



math \text{D. \indent}\\ math

Click here for solution.

math \text{What is the equation to this graph?} math
 * Question 2**



math \\ \text{A.} \indent r(\theta)=2\sin(5\theta) \\ \text{B.} \indent r(\theta)=-2\cos(5\theta)\\ \text{C.} \indent r(\theta)=2\sin(10\theta)\\ \text{D.} \indent r(\theta)=2\cos(5\theta)\\ math

Click here for solution.

math \text{How many rose petals does this rose have? } r(\theta)=101\sin(45\theta)\\ \text{A.} \indent 101\\ \text{B.} \indent 45\\ \text{C.} \indent 90\\ \text{D.} \indent 146\\ math
 * Question 3**

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math \text{Convert the following polar equation into rectangular form: } r=5-7\cos\theta\\ \text{A.} \indent 101 \\ \text{B.} \indent \\ \text{C.} \indent x^{2}+y^{2}=5\sqrt{x^{2}+y^{2}} -7x \\ \text{D.} \indent x^{2}+y^{2}=5\sqrt{x^{2}+y^{2}} -7y math Click here for solution.
 * Question 4**

math \text{Convert the following rectangular equation to polar form:} \\
 * Question 5**

\text{What does} 3+8\cos\theta \text{ look like?} math

math \text{A. \indent}\\ math math \text{B. \indent}\\ math

math \text{C. \indent}\\ math



Click here for solution.

math \text{Convert the following equation to polar form:} \[2x ^{2} + 2y ^{2} - x + y = 0\]\\ \text{A.}\indent 2r - \cos\theta + \sin\theta = 0\\ \text{B.}\indent r- 2 \cost\theta + 2 \sin\theta = 0\\ \text{C.}\indent \cos\theta + \sin\theta = 0\\ \text{D.}\indent 2r - 2 \cos\theta + 2 \sin\theta = 0\\ math Click here for solution.
 * Question 6**

math \text{Which of the following equations are not in the graph below?} math
 * Question 7**

math \\ \text{A.} \indent r(\theta)=5+4\cos((\theta) \\ \text{B.} \indent r(\theta)=5+4\cos\((2\theta) \\ \text{C.} \indent r(\theta)=5+4\cos\((3\theta) \\ \text{D.} \indent r(\theta)=5+4\cos\((4\theta) \\ math Click here for solution.

math \text{What is the equation for this graph?} math math \\ \text{A.} \indent r(\theta)=5+4\cos((6\theta) \\ \text{B.} \indent r(\theta)=2+1\sin((3\theta) \\ \text{C.} \indent r(\theta)=1+2\cos((3\theta) \\ \text{D.} \indent r(\theta)=1-2\sin((3\theta) \\ math Click here for solution.
 * Question 8**

math \text{What equations recreate this cardioid limacon graph?} math
 * Question 9**

math \\ \text{A.} \indent r(\theta)=3-3\sin(\theta) \\ \text{B.} \indent r(\theta)=3+3\sin(\theta) \\ \text{C.} \indent r(\theta)=-3-3\sin(\theta) \\ \text{D.} \indent r(\theta)=-3+3\sin(\theta) math Click here for solution.

Graph this equation: math \\r(\theta)=10\sin(\theta) math A. B. C. D. Click here for solution.
 * Question 10**

math \text{Which is NOT a way to express this point on the Cartesian plane in polar form? } (5\sqrt{3},5)\\ \text{A.} \indent (10, \frac{\pi}{6})\\ \text{B.} \indent (-10,\frac{7\pi}{6}) \\ \text{C.} \indent (10,\frac{-11\pi}{6}) \\ \text{D.} \indent (-10,\frac{-7\pi}{6}) math
 * Question 11**

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math \text{Which of the following equations does not represent a graph of the line with a slope of 3 and that goes through the point} (4,6)\\ \text{A.} \indent r(\theta)= \frac{-6}{sin\theta-3cos\theta} \\ \text{B.} \indent y= 3x-12 \\ \text{C.} \indent r(\theta)= \frac{sin\theta-3cos\theta}{6} \\ \text{D.} \indent y-6 = 3(x-4) math
 * Question 12**

Click here for solution.

Consider the following graph:
 * Question 13**

math \text{Given that the r value of the larger leaves are 6 and -6, and that the r values of the smaller leaves are -2 and 2, find the equation for this graph.}\\ \text{A.}\indent r(\theta)=2+4sin(2\theta)\\ \text{B.}\indent r(\theta)=4+2sin(2\theta)\\ \text{C.}\indent r(\theta)=2+4cos(2\theta)\\ \text{D.}\indent r(\theta)=4+2cos(2\theta)\\ math Click here for solution.

math \text{Which of the following represents a rose graph with 14 pedals?} \\ \text{A.} \indent r(\theta)=12sin7\theta \\ \text{B.} \indent r(\theta)=14sin\theta \\ \text{C.} \indent r(\theta)=7sin14\theta\\ \text{D.} \indent \text{None of the above}
 * Question 14**

math

Click here for solution.

Convert (5,8) to Polar form. (in Radians) math \text{A.}\indent (9.43, 58)\\ \text{B.}\indent (9.43, 1.01)\\ \text{C.}\indent (9.43, .55)\\ \text{D.}\indent (9.43, 100000)\\ math Click here for solution.
 * Question 15**

Convert (8, π) to rectangular form math \text{A.}\indent (8, 0)\\ \text{B.}\indent (8, 8)\\ \text{C.}\indent (-8, 0)\\ \text{D.}\indent (-8, -8)\\ math
 * Question 16**

Click here for solution.

=Primary Authors=
 * Tyler Klivickis**
 * Thomas Kaszuba**
 * Jerry Pan**
 * Sam Lee**
 * Kirk Halverson**
 * Jay Wang**