2 4 a b 1 3correct 5 a b 3 16 a b 1 37 a b 2 38 a b 3 1Explanation Since the

2 4 a b 1 3correct 5 a b 3 16 a b 1 37 a b 2 38 a b 3

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2)4.(a, b) = (1,3)correct5.(a, b) = (3,1)6.(a, b) = (-1,3)7.(a, b) = (-2,3)8.(a, b) = (3,-1)Explanation:Since the relationship between Cartesiancoordinates and polar coordinates isx=rcosθ ,y=rsinθ ,the pointP(2, π/3) is given in Cartesian co-ordinates byP(2, π/3) =parenleftBig2 cosπ3,2 sinπ3parenrightBig= (1,3).keywords: polar coordinates, Cartesian coor-dinates01010.0pointsFind a polar equation for the curve givenby the Cartesian equation2y=x2.1.2r= secθtanθ2.r= 2 cscθtanθ3.r= 2 cscθcotθ4.2r= secθcotθ5.2r= cscθcotθ6.r= 2 secθtanθcorrectExplanation:We have to substitute forx, yin2y=x2using the relationsx=rcosθ ,y=rsinθ .In this case the Cartesian equation becomes2rsinθ=r2cos2θ .Consequently, the polar form of the equationisr= 2 secθtanθ.
pacheco (jnp926) – Homework 8 – staron – (52840) 6 011 10.0points Find a Cartesian equation for the curvegiven by the polar equationr+ 8 sinθ= 0. 01210.0pointsWhich one of the following could be thegraph of the polar curver= 2 cscθ? 1.correct 5.
pacheco (jnp926) – Homework 8 – staron – (52840) 7 6. Explanation: As is sometimes the case with polar curves, it is more convenient to use the relations x = r cos θ , y = r sin θ , to convert the polar form to Cartesian form. For then r = 2 csc θ = 2 sin θ becomes y = 2 in Cartesian form. Thus the graph of r = 2 sec θ is the horizontal line keywords: polar graph, polar curve, convert to Cartesian form, line, circle, 013 10.0points 1. r = 2 cos θ 2. r = 2 sec θ 3. r = 2 sin θ 4. θ = 2 5. r = 2 csc θ 6. r = 2 correct Explanation: When the graph of a polar function cannot be determined directly, it is sometimes more convenient to use the relations x = r cos θ , y = r sin θ , to convert the polar form to Cartesian form and then use standard knowledge of Cartesian graphs. This is often the case with special lines and circles, so let’s look at the six polar functions listed above. 1. InCartesianform r = 2 sec θ = 2 cos θ becomes x = 2 anditsgraphisaverticalline totherightoftheorigin .
pacheco (jnp926) – Homework 8 – staron – (52840) 8

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