12. ⎛ 1 3 ⎞ 1 3 ⎛ 1 2 6 ⎞ 1 2 6 14. = ⎜ , − ⎟ ⇒ = , = − = ⎜ − , ⎟ ⇒ = − , = P x y P x y ⎝ 2 2 ⎠ 2 2 ⎝ ⎠ 5 5 5 5 = = − sin 3 t y 2 sin = = 2 6 t y 5 =− 5 cos = = 1 t x ⎛ ⎞ 2 6 2 cos = t x ⎛ 3 ⎞ 1 − ⎜ ⎟ ⎜ ⎟ ⎛ ⎞ = = ⎝ − ⎟ − tan 5 = 2 6 t y 3 ⋅ 2 = tan = = 5 ⎠ = 2 6 ⎜ t y 2 ⎠ = − − 3 ⎝ ⎛ ⎞ 1 2 1 x ⎛ 1 ⎞ 5 ⎝ 1 ⎠ x ⎜ ⎟ ⎝ ⎠ ⎜ − ⎟ ⎝ 5 ⎠ csc = 1 = 1 = − 2 = − 2 ⋅ 3 = − t csc = 1 = 1 = 1⋅ 5 = 5 ⋅ 6 = 5 6 t 2 3 ⎛ 3 ⎞ y 2 6 2 6 6 12 3 3 3 3 ⎛ 2 6 ⎞ y − ⎜ 2 ⎟ ⎜ 5 ⎟ ⎝ ⎠ ⎝ ⎠ = = = = sec 1 1 1⋅ 2 t sec = 1 = 1 = 1⎛ − 5 ⎞ = t 2 −5 ⎛ ⎞ 1 1 x ⎜ ⎟ 1 1 x ⎜ ⎟ ⎛ − ⎞ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎛ ⎞ 1 ⎛ 1 ⎞ ⎜ ⎟ ⎜ − ⎟ ⎛ ⎞ = = cot t x 1 2 1 =− ⎝ 2 ⎠ cot = = ⎝ 5 ⎠ = − 1 ⎜ 5 ⎟ =− t x 3 3 ⋅ ⎛ 3 ⎞ y 5 ⎝ 2 6 ⎠ 2 3 3 3 3 ⎛ 2 6 ⎞ y − ⎜ ⎟ 2 ⎜ 5 ⎟ ⎝ ⎠ ⎝ ⎠ = − 1 ⋅ 6 = − 6 13. ⎛ 2 21 ⎞ 2 21 2 6 6 12 = ⎜ − , ⎟ ⇒ = − , = P x y ⎝ 5 5 ⎠ 5 5 2 2 ⎞ 2 2 sin = = 21 t y = − , ⇒ = − , = P x y ⎛ 15.
12. ⎛ 1 3 ⎞ 1 3 P = ⎜ , − ⎟ ⇒ x = , y = − 14. ⎛ 1 2 6 ⎞ 1 2 6 P = ⎜ − , ⎟ ⇒ x = − , y = ⎝ 2 2 ⎠ 2 2 ⎝ 5 5 ⎠ 5 5 sin t = y = − 3 2 sin t = y = 2 6 5 cos t = x = 1 2 ⎛ 3 ⎞ − cos t = x 1 =− 5 ⎛ 2 6 ⎞ ⎜ ⎟ ⎜ ⎟ ⎛ ⎞ tan t = y = ⎝ 2 ⎠ = − 3 ⋅ 2 = − 3 tan t = y = ⎝ 5 ⎠ = 2 6 ⎜ − 5 ⎟ = − 2 6 x ⎛ 1 ⎞ 2 1 x ⎛ 1 ⎞ 5 ⎝ 1 ⎠ ⎜ ⎟ ⎝ ⎠ csc t = 1 = 1 = − 2 = − 2 ⋅ 3 = − 2 3 ⎜ − ⎟ ⎝ 5 ⎠ csc t = 1 = 1 = 1⋅ 5 = 5 ⋅ 6 = 5 6 y ⎛ 3 ⎞ − 3 3 3 3 y ⎛ 2 6 ⎞ 2 6 2 6 6 12 ⎜ 2 ⎟ ⎜ 5 ⎟ ⎝ ⎠ sec t = 1 = 1 = 1⋅ 2 = 2 ⎝ ⎠ sec t = 1 = 1 = 1⎛ − 5 ⎞ = −5 x ⎛ 1 ⎞ 1 x 1 ⎜ 1 ⎟ ⎜ ⎟ ⎛ − ⎞ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎛ 1 ⎞ ⎛ 1 ⎞ ⎜ ⎟ ⎜ − ⎟ ⎛ ⎞ cot t = x = ⎝ 2 ⎠ 1 2 1 =− ⋅ 3 =− 3 cot t = x = ⎝ 5 ⎠ = − 1 ⎜ 5 ⎟ y ⎛ 3 ⎞ − 2 3 3 3 3 y ⎛ 2 6 ⎞ 5 ⎝ 2 6 ⎠ ⎜ 2 ⎟ ⎜ 5 ⎟ ⎝ ⎠ ⎝ ⎠ = − 1 ⋅ 6 = − 6 13. ⎛ 2 21 ⎞ 2 21 P = ⎜ − , ⎟ ⇒ x = − , y = 2 6 6 12 ⎝ 5 5 ⎠ 5 5 sin t = y = 21 15. ⎛ 2 2 ⎞ 2 2 P = − , ⇒ x = − , y =
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