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Here are some tests that we can use to help determine whether a polar graph has certain symmetries. Symmetry with respect to the polar axis If replacing (r.) by (r. - 0) or (-r,л- 0) results in an equivalent equation, the polar graph is symmetric with respect to the polar axis. Symmetry with respect to the line 0 = T 2 If replacing (r, 0) by (г, л-0) or (-r. - 0) results in an equivalent equation, the polar graph is symmetric with respect to π the line 0 = 2 Each test is sufficient to prove the symmetry but is not necessary. That is, a polar equation may fail the test but still have the symmetry. For each polar equation, check all symmetries that are guaranteed by only the tests above. Symmetry with respect to the pole If replacing (r, 0) by (r, л+0) or (-r, 0) results in an equivalent equation, the polar graph is symmetric with respect to the pole. Aa Symmetry: 0 r = 2 cos 50 Polar axis Line = Pole π 2 None of these symmetries is guaranteed by the tests above. Symmetry: 0 Polar axis Line = r=4sin 0 Pole Espanor Է 2 ? None of these symmetries is guaranteed by the tests above.

Here are some tests that we can use to help determine whether a polar graph has certain symmetries. Symmetry with respect to the polar axis If replacing (r.) by (r. - 0) or (-r,л- 0) results in an equivalent equation, the polar graph is symmetric with respect to the polar axis. Symmetry with respect to the line 0 = T 2 If replacing (r, 0) by (г, л-0) or (-r. - 0) results in an equivalent equation, the polar graph is symmetric with respect to π the line 0 = 2 Each test is sufficient to prove the symmetry but is not necessary. That is, a polar equation may fail the test but still have the symmetry. For each polar equation, check all symmetries that are guaranteed by only the tests above. Symmetry with respect to the pole If replacing (r, 0) by (r, л+0) or (-r, 0) results in an equivalent equation, the polar graph is symmetric with respect to the pole. Aa Symmetry: 0 r = 2 cos 50 Polar axis Line = Pole π 2 None of these symmetries is guaranteed by the tests above. Symmetry: 0 Polar axis Line = r=4sin 0 Pole Espanor Է 2 ? None of these symmetries is guaranteed by the tests above.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter8: Complex Numbers And Polarcoordinates
Section: Chapter Questions
Problem 7GP
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Here are some tests that we can use to help determine whether a polar graph has certain symmetries. Symmetry with respect to the polar axis If replacing (r, 0) by (r, − 0) or (−˜‚ à – 0) results in an equivalent equation, the polar graph is symmetric with respect to the polar axis. the line = - Symmetry with respect to the line If replacing (r, 0) by (г, è −0) or (-r, −0) results in an equivalent equation, the polar graph is symmetric with respect to ♫ 2 Symmetry with respect to the pole If replacing (r, 0) by (˜‚ à + ¤) or ( −˜, 0) results in an equivalent equation, the polar graph is symmetric with respect to the pole. pect to Aa Each test is sufficient to prove the symmetry but is not necessary. That is, a polar equation may fail the test but still have the symmetry. For each polar equation, check all symmetries that are guaranteed by only the tests above. Symmetry: r = 2 cos 50 Polar axis Line Pole π 2 = ♫ 2 None of these symmetries is guaranteed by the tests above. Symmetry: Polar axis Line r = 4 sin 0 Pole EN ? 플 None of these symmetries is guaranteed by the tests above. |>]
Transcribed Image Text:Here are some tests that we can use to help determine whether a polar graph has certain symmetries. Symmetry with respect to the polar axis If replacing (r, 0) by (r, − 0) or (−˜‚ à – 0) results in an equivalent equation, the polar graph is symmetric with respect to the polar axis. the line = - Symmetry with respect to the line If replacing (r, 0) by (г, è −0) or (-r, −0) results in an equivalent equation, the polar graph is symmetric with respect to ♫ 2 Symmetry with respect to the pole If replacing (r, 0) by (˜‚ à + ¤) or ( −˜, 0) results in an equivalent equation, the polar graph is symmetric with respect to the pole. pect to Aa Each test is sufficient to prove the symmetry but is not necessary. That is, a polar equation may fail the test but still have the symmetry. For each polar equation, check all symmetries that are guaranteed by only the tests above. Symmetry: r = 2 cos 50 Polar axis Line Pole π 2 = ♫ 2 None of these symmetries is guaranteed by the tests above. Symmetry: Polar axis Line r = 4 sin 0 Pole EN ? 플 None of these symmetries is guaranteed by the tests above. |>]
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