8.7+OFSA+Solutions


 * OFSA SOLUTIONS for Polar Graphs**

This page contains peer generated solutions and error explanations to OFSA questions. As you read or view the solutions, be critical: check for accuracy, but also for more efficient solution strategies. If you have a better method or different idea/answer, post a discussion and monitor the responses.


 * Quick Directions**
 * Post answers, solutions and error explanations to each OFSA question below.
 * For each "distractor" or incorrect answer choice, explain the error that would lead to that incorrect answer choice.
 * You may either do the above in typed format or using a pencast.
 * Separate each question with a section bar.
 * After each solution, provide a hyperlink back to the corresponding OFSA page.
 * Follow example below.
 * Click here to refer to solution format in 7.7


 * Question 1**
 * __Solution 1__**

Click here to return to OFSA
 * __Error Explanation 1__**

.

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

math \boxed{\text{D.} \indent r(\theta)=2\cos(5\theta)}\\ math math \begin{array}{*{20}{l}} &{r(\theta)=2\sin(5\theta)}& \\ &{r(\theta)=-2\cos(5\theta)}&{{\text{Error. Student did not check the starting point (0,2) correctly}} \\ &{r(\theta)=2\sin(10\theta)}& \\ &{r(\theta)=2\cos(5\theta)}& \\
 * __Solution 2__**
 * __Error Explanation 2__**

\end{array} math

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math \text{How many rose petals does this rose have? } r(\theta)=101\sin(45\theta)\\ math math \boxed{\text{B.} \indent 45}\\ math math \begin{array}{*{20}{l}} &{101}& \\ &{45}& \\ &{90}& \\ &{146}& \\ \end{array} math
 * Question 3**
 * __Solution 3__**
 * __Error Explanation 3__**

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math \text{Convert the following polar equation into rectangular form: } r=5-7\cos\theta\\ math
 * Question 4**

math \begin{gathered} \\ r=5-7\cos\theta \hfill \\ \text{Step 1:} \indent r=5-7(\frac{x}{r}) \hfill \\ \text{Step 2:} \indent r^{2}=5r-7x \hfill \\ \text{Step 3:} \indent \boxed{x^{2}+y^{2}=5\sqrt{x^{2}+y^{2}}-7x} \hfill \\ \end{gathered} math
 * __Solution 4__**

math \begin{array}{*{20}{l}} &{101}& \\ &{101}& \\ &{x^{2}+y^{2}=5\sqrt{x^{2}+y^{2}}-7x}& \\ &{x^{2}+y^{2}=5\sqrt{x^{2}+y^{2}}-7y}& \cos\theta=\frac{y}{r} \\ \end{array} math
 * __Error Explanation 4__**

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 * Question 5**
 * __Solution 5__**


 * __Er__****__ror Ex__****__p__****__lanation 5__**

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math \text{A.}\indent \[2r - \cos\theta + \sin\theta = 0 \]\\ math math \text{If the student mis-factors, the resulting answer will be wrong}
 * Question 6**
 * __Solution 6__**
 * __Error Explanation 6__**

math

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

math \D\:\ \text{D)} \indent r(\theta)=5+4\cos\4\theta math
 * __Solution 7__**

math \text{the equation's k value increases by an increment of 1 each time. It starts with the dimple graph, but as it goes up, it becomes a rose graph. There is no eight leaved petal} math
 * __Error Explanation 7__**

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math \text{What is the equation for this graph?} math
 * Question 8**



math \text{So to get the equation, the middle between each petal is 2, so because the rose graph is on the y-asymptote, it is a sin graph. After you get those variables of the equation} math math \text{all you need now is to understand that the petals are spaced one away from the middle so it is } math math r(\theta1)=1-2\sin(\3\theta) math
 * __Solution 8__**
 * __Error Explanation 8__**

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math \text{What is the equation for this cardioid limacon graph?} math
 * Question 9**

math \text{the answer is A and C.} math math \\ \text{A. CORRECT} \\ \text{B. This would make the graph point up instead of down} \\ \text{C. CORRECT} \\ \text{D. This would also make the graph point up instead of down} \\ math
 * __Solution 9__**
 * __Error Explanation 8__**

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The answer is A. math \\r(\theta)=-10\sin(\theta) math
 * Question 10**
 * __Solution 10__**
 * __Error Explanation 10__**
 * B is wrong because it is the opposite way, it would be the graph to **
 * C and D are both wrong because they are cosine graphs. **

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math \text{Which is NOT a way to express this point on the Cartesian plane in polar form? } (5\sqrt{3},5)\\ math D Answer choice D puts the point in quadrant 4, but the point is in quadrant 1.
 * Question 11**
 * __Solution 11__**
 * __Error Explanation 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} math C The easiest way to do this is to first write the equation in rectangular form, then convert to polar form. Answer choices B and D both are equivalent, so one of the polar equations must be incorrect. If you convert the equation to polar form, you see that A is also correct, so C must be the correct answer choice.
 * Question 12**
 * __Solution 12__**
 * __Error Explanation 12__**

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The correct answer is A. This problem is more of a plug in problem. Plug in 0 pi, find the output, and see which would match the graph. The others do not, so it must be A.
 * Question 13**
 * __Solution 13__**
 * __Error Explanation 13__**

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math \text{Which of the following represents a rose graph with 14 pedals?} \\ math D We know for rose graphs, the number of pedals is determined by the coefficient in front of theta. However, using that knowledge, there is no way to create a rose graph with 14 pedals. 14 divided by 2 is an odd number, and 14 is even, so the coefficient can't be even or odd. Therefore, the only way to make a 14 pedaled rose is to have multiple graphs.
 * Question 14**
 * __Solution 14__**
 * __Error Explanation 14__**

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math \text{B.}\indent (9.43, 1.01)\\ math
 * Question 15**
 * __Solution 15__**

math \\ \text{A.}\indent (9.43, 58) \; \text{Student is in degrees}\\ \text{B.}\indent (9.43, 1.01)\; \text{CORRECT}\\ \text{C.}\indent (9.43, .55) \; \text{Student took } cot^{-1}\\ \text{D.}\indent (9.43,100000) \; \text{Student is in wrong class}\\ math
 * __Error Explanation 15__**

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math \text{C.}\indent (-8, 0)\\ math math \\ \text{A.}\indent (8, 0)\,\text{Simple error}\\ \text{B.}\indent (8, 8)\,\text{Incorrect evaluation of sin}\\ \text{C.}\indent (-8, 0)\,\text{CORRECT}\\ \text{D.}\indent (-8, -8)\,\text{Error}\\ math
 * Question 16**
 * __Solution 16__**
 * __Error Explanation 16__**

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