• Franklin Academy High School

• MATH 1107

Avon High School SOLUTIONS AP Calculus BC Polar Equations and Calculus Period _______ Score _______ / 18 For each of the following problems, do not use your calculator unless you see the calculator icon. Credit will only be given for correct answers with adequate supporting work. 1. Convert the rectangular equation 2 y x = 9 to polar form. (A) 2 r = 3csc cos   (B) 3cos sin r   = (C) 2 r = 9csc cos   (D) 2 r = 9sin cos   2 2 2 2 2 9cos C. sin 9 cos sin 9cos 9csc cos sin r r r r r         =  =  =  = 2. Convert the polar equation r = + sec csc   to rectangular form. (A) 1 r x = − (B) 1 r x = (C) 1 x r x = − (D) 1 x r x = + ( ) C. 1 r r ry rx r y x r r r xy x y x y xy xy x xy y x y x + + = +  =  =  = + − =  = − 3. For the polar curve r = −3 4sin , find dy dx at  = 0. (A) 3 4 − (B) 3 4 (C) 4 3 − (D) 4 3 ( ) ( )( ) ( ) ( ) ( ) ( )( ) ( ) ( ) 0 0 cos 3 4sin cos sin 3 4sin sin A. 3 4sin sin cos 4cos 3 4sin cos sin 4cos 0 1 4 4 3 1 0 3 3 4 x r y r dx dy d d dx dy d d dy dy d dx ds d                       = = = = − = = − = − − + − = − + − = + − = − = + = − = = This study source was downloaded by 100000899606070 from CourseHero.com on 03-09-2026 07:44:31 GMT -05:00 https://www.coursehero.com/file/221124019/Unit-9B-Polar-Equations-and-Calculus-MCQ-Enrichment-SOLUTIONSpdf/ 4. Find the equation of the line tangent to r = +2 3sin at  = . (A) ( ) 2 2 3 y x = − (B) ( ) 2 2 3 y x = − + (C) ( ) 3 2 2 y x = − + (D) ( ) 3 2 2 y x = − ( ) ( )( ) ( )( ) ( ) ( )( ) ( )( ) ( ) ( )( ) ( )( ) ( ) ( )( ) ( ) cos 2 3sin cos sin 2 3sin sin 2 0 1 2 2 0 0 0 B. 2 3sin sin cos 3cos 2 3sin cos sin 3cos 2 0 0 1 3 3 2 0 1 0 3 2 2 Tangent l 3 x r y r x y dx dy d d dx dy d d dy dy d dx dx d                             = = = = = = + = = + = + − = − = + = = + − + = + + = + + − − = = + − + − = − = = − ( ) 2 ine: 2 3 y x = − + 5. The graph of the four-leaf rose r