Section 9.5

1. Fill in each blank so that the resulting statement is true. The pair 01 equations 3: = \"if? and y = 2t -1 are called equations and the common variable t is called the . The graph of this pair of equations is called sin] The pair 01 equations :4 = 4ft- and y = 2t -1 are called (1} equations and the common variable t is called the {2) The graph of this pair of equations is called a [3) {1} \":1 parametric {2} if} parameter. {3} iii parameter. C:- plane curve if) plane curve. C! plane curve. {:1- parameter 5:} parametric. Ci parametric. 2. Fill in each blank so that the resulting statement is true. In order to eliminate the parameter from x =3sint and y = 2 cost. isolate and . square the two equations. and then use the identity In order to eliminate the parameter from 3: =35th and y = 2 cos t, isolate {'Ij and {2} _ square the two equations, and then use the identity {3) (1] 1:: x {2] f) 3 [3} '3 sin2t=25inteost [.3 sint 5:} 2 \"j sin2t+ cuszt=1. :21 Ct cost 1- cos 2t y .J sin2t=T cos 2t= cos 2t- sin 2t -:; LI 3. Fill in the blank so that the resulting statement is true. True orlalee: There is more than one way for pairs of parametric equations to represent the same plane curve. {1} {1} C:- False. C: True. 4. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value oft. lt=3t+5.y= -3t+2: [=2 The ordered pair is . {$implify your answer. Type an ordered pair.) 5. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x=17+7, y=5-1; t=3 What are the coordinates of the point? (Simplify your answer. Type an exact answer, using radicals as needed. Type an ordered pair.)6. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. x = (60 cos 30")t, y = 7 + (60 sin 30")t - 11t ; t= 2 What are the coordinates of the point? (Simplify your answer. Type an exact answer, using radicals as needed. Type an ordered pair.) 7. In the following exercise eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. x= t, y= - 5t; - co