16. ⎛ 2 2 ⎞ 2 2 ⎛ 2 2 ⎞ = ⎜ , ⎟ ⇒ = , = P x y ⎜ ⎟ ⎛ ⎞ ⎝ ⎠ 2 2 2 2 cot = = ⎝ 3 ⎠ = 2 2 ⎜ − 3 ⎟ = −2 2 t x ⎛ − 1 ⎞ y ⎝ ⎠ 3 1 sin = = 2 t y ⎜ 3 ⎟ 2 ⎝ ⎠ cos = = 2 t x 5 2 ⎛ 5 2 ⎞ = − 2 18. 3 3 − , , ⇒ x y = ⎜ − P = − 3 3 ⎛ ⎞ ⎝ ⎠ 2 ⎝ ⎠ y = sin 2 t y tan = = = 1 3 t ⎛ 2 ⎞ x ⎜ 2 ⎟ cos = = − 5 t x ⎝ ⎠ 3 csc = 1 = 1 = 1⋅ 2 = 2 ⋅ 2 = t ⎛ 2 ⎞ ⎜ ⎟ 2 ⎛ 2 ⎞ y tan = = ⎝ 3 ⎠ = − 2 ⎛ − 3 ⎞ t y 2 2 2 ⎜ 2 ⎟ 3 ⎜ 5 ⎟ ⎛ 5 ⎞ x ⎝ ⎠ ⎜ − ⎟ sec = 1 = 1 = 1⋅ 2 = 2 ⋅ 2 = 2 ⎝ ⎠ t ⎛ 2 ⎞ x 2 2 2 = 2 ⋅ 5 = 2 5 ⎜ ⎟ 2 5 5 5 ⎝ ⎠ ⎛ 2 ⎞ csc = 1 = 1 = 1⎛ − 3 ⎞ = − 3 t ⎜ ⎟ y ⎜ ⎟ 2 ⎛ 2 ⎞ 2 ⎝ ⎠ 2 x ⎜ − ⎟ ⎝ ⎠ cot = = t = 1 ⎝ 3 ⎠ ⎛ ⎞ 2 y ⎜ ⎟ 2 = = = − ⎞ sec 1 1 1⎛ 3 t ⎝ ⎠ ⎛ 5 ⎞ ⎜ 5 ⎟ x ⎝ ⎠ ⎜ − 3 ⎟ 17. ⎝ ⎠ ⎛ 2 2 1 ⎞ 2 2 1 3 5 3 5 = ⎜ , − ⎟ ⇒ = , = − P x y ⎝ 3 3 ⎠ 3 3 =− ⋅ = − 5 5 5 sin = = − 1 t y 3
16. ⎛ 2 2 ⎞ 2 2 P = ⎜ , ⎟ ⇒ x = , y = ⎛ 2 2 ⎞ ⎜ ⎟ ⎛ ⎞ ⎝ 2 2 ⎠ 2 2 cot t = x = ⎝ 3 ⎠ = 2 2 ⎜ − 3 ⎟ = −2 2 y ⎛ − 1 ⎞ 3 ⎝ 1 ⎠ sin t = y = 2 ⎜ 3 ⎟ 2 cos t = x = 2 ⎝ ⎠ ⎛ 5 2 ⎞ 5 2 2 18. P = ⎜ − , − ⇒ x = − 3 3 , y = − 3 3 ⎛ 2 ⎞ ⎝ ⎠ y ⎝ ⎠ sin t = y 2 tan t = = = 1 3 x ⎛ 2 ⎞ ⎜ 2 ⎟ cos t = x = − 5 ⎝ ⎠ csc t = 1 = 1 = 1⋅ 2 = 2 ⋅ 2 = 2 3 ⎛ 2 ⎞ ⎜ ⎟ y ⎛ 2 ⎞ 2 2 2 tan t = y = ⎝ 3 ⎠ = − 2 ⎛ − 3 ⎞ ⎜ 2 ⎟ x ⎛ 5 ⎞ 3 ⎜ 5 ⎟ ⎝ ⎠ ⎜ − ⎟ sec t = 1 = 1 = 1⋅ 2 = 2 ⋅ 2 = 2 ⎝ ⎠ x ⎛ 2 ⎞ 2 2 2 = 2 ⋅ 5 = 2 5 ⎜ 2 ⎟ 5 5 5 ⎝ ⎠ ⎛ 2 ⎞ csc t = 1 = 1 = 1⎛ − 3 ⎞ = − 3 ⎜ ⎟ y ⎛ 2 ⎞ ⎜ 2 ⎟ 2 x ⎝ 2 ⎠ ⎜ − ⎟ ⎝ ⎠ cot t = = = 1 ⎝ 3 ⎠ y ⎛ 2 ⎞ ⎜ 2 ⎟ sec t = 1 = 1 = 1⎛ − 3 ⎞ ⎝ ⎠ x ⎛ 5 ⎞ ⎜ 5 ⎟ ⎝ ⎠ ⎜ − 3 ⎟ 17. ⎛ 2 2 1 ⎞ 2 2 1 P = ⎜ , − ⎟ ⇒ x = , y = − ⎝ ⎠ 3 5 3 5 ⎝ 3 3 ⎠ 3 3 =− ⋅ = − 5 5 5 sin t = y = − 1 3