Question: Explain why the following test for symmetry is valid: Replace r by -r and by - in a polar equation. If an equivalent

Explain why the following test for symmetry is valid: Replace r by -r and θ by -θ in a polar equation. If an equivalent equation results, the graph is symmetric with respect to the line θ = π/2 (y-axis).

(a) Show that the test fails for r²= cosθ yet this new test works.

(b) Show that the test works for r²= sinθ yet this new test fails.

Step by Step Solution

★★★★★

3.41 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a r cose r cos0 r cos 8 Not equi... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Explain why the following hypotheses are not constructed correctly. a. H0: 10; HA: 10 b. H0: 500; HA: = 500 c. H0 : p 0.40; HA: p > 0.42 d. H0 : 128; HA: > 128

Explain why the following functions F: R2 R2 are not linear. (a) (b) (c) (d) (e) 2y (Ix) lyl sin(xy) 2x + y

Explain why the following statements are not correct. a. With my methodological approach, I can reduce the Type I error with the given sample information without changing the Type II error. b. I have...

12.C. a. Explain what a student must do to test for the three symmetries of a polar graph. b. Suppose you are testing the symmetry of a polar graph, for instance symmetry with respect to the pole....

The conditions for symmetry given in the text are sufficient conditions, not necessary conditions. Give an example of a polar equation r = f () whose graph is symmetric with respect to the y-axis,...

someone help show all work on paper some help everth in the pictures is what gots to get don. SHOW ALL WORK ON PAPER COMPLETE aLL THE PROBLEMS Complete PROBLEMS 2-81 thru 2-84 and 2-89, 2-91 thru...

1. Complete the sentence below. In polar coordinates. the graphs of r2 a cos 8 and r = a sin 9 are In polar coordinates, the graphs of r= a c058 and r = a sin 8 are (1) {1) C3 roses. ' '- limaoons....

question 11-22 744 Chapter 11 Analytic Geometry In Exercises 11-16, convert the rectangular coordinates 48. a. Find a complete graph of r = 1 - 3 sin 26 b. Predict what the graph of r = 1 3 sin 30 wi...

Help please huhu as much as possible computerized solution so that i can read and undertand clearly, thank you so much THEOREM 8.2.1 Tests for Symm- Thc graph of a polar equation is symmetric with...

please show all the work let me understand your hand writing thank you Objective 1: Graph Polar Equations by Plotting Points For Exercises 7. 14, graph the polar equation. (See Example 1) '7. r = 3...

Because government policymakers do not consider inflation desirable, their policies cannot be the source of inflation. Is this statement true, false, or uncertain? Explain your answer.

Graph: for x-1, x-1, for x > 1

15.40 In a class survey done in a statistics class, students were asked, Suppose that you are buying a new car and the model you are buying is available in three colors: silver, blue, or green. Which...

4. Participate in standards development, conformance assessment and review.

For the following exercises, solve the system of nonlinear equations. y = x 2 4 y = 5x + 10

For the following exercises, use the matrices below to perform matrix multiplication. DC A=[- 5], B =[ 3 3 3 6 -8 0 4 10] 2 TP-6 6, D = 9 9 12].C=[-2 5 -3 33 0 8 12] 1 -10]

For the following exercises, use any method to solve the system of nonlinear equations. x - x = y x + y = 0

The Aleutian Company produces two products, Rings and Dings. They are manufactured in two departments, Fabrication and assembly. Data for the products and departments are listed below. Product Number...

You have been asked by the President of your company to evaluate the proposed acquisition of a new spectrometer for the firm's R&D department. The equipment's basic price is $70,000, and it would...

Preferably in excel with formulas please The cooked up spread. You have been doing research on General Electric Company (GE). You note that Ford is currently trading at $6.43. After doing some...