3. Simplify the following, giving the results in polar form (1) 3(cos 143° + j sin 143°) X 4(cos 57° +j sin 57°) 10(cos 126° + j sin 126°) (ii) 2(cos 72° +j sin 72°)

Q: 6. What is the equation of the polar curve shown? a) r = -4 sin 30 c) r = 4 cos 30 b) r = 4 sin 30…

A: Since you have asked multiple question so we will be answering only first question. Given polar…

Q: 24/ Replace the polar equation r. sin (0 +") = 2 to Cartesian equation -(G+ ns./ = 2

A: The given polar equation is r·sinθ+π6=2 .................(1)

Q: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) 9 + 7i r = • 0…

A: The given complex number is: z=9+7i

Q: 1 By first changing to polar coordinates, evaluate 1+ x + y dA, where R is the quarter-disk region…

A: Given integral is ∫1+x2+y2dA over the region R where R is quarter disk region shaded above. Use the…

Q: Which one of the following polar equations is equivalent to y=x -4. 4 r = cos 0 – sin 0 cos 0 – sin…

A:

Q: Evaluate the following and express the result in polar form. Note: Solve problem number 13 only.…

A: Any complex number z=x+jy can be presented in its polar form as z=r(cosθ+jsinθ) , where, r=x2+y2 and…

Q: Find a Cartesian equation from the polar curve 4r sin 0 = 18(rcos 0) +14 1S is

A: Given polar equation is 4rsinθ=18rcosθ2+14  .....1

Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² - 4x=0 O A. r cos²0=4 sin…

A:

Q: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

Q: 3) Convert the following polar equations to rectangular equations. 1 a) r = b. r=4 4 cos 0-3 sin 0

A: (a)r=14cosθ-3sinθSince, x=r cosθ , y=r sinθso,cosθ=xr , sinθ=yrsubstitute in the given polar…

Q: Find zw and z/w, Leave your answers in polar form.

A: Given the complex numbers  z=2(cos5π3+isin5π3)w=3(cosπ3+isinπ3)

Q: 6. O Convert the quation aty z+y froui cartesian to polar (10 P.) (u) Convert the equation r - 2 sme…

A:

Q: Consider the polar equation defined by r = 5 cos(2 sin 6), where 0<0< 27. Determine the missing…

A:

Q: Q1) A) Replace the polar equation r? sin 20 = 2 by equivalent Cartesian equation. B; C) Find the…

A:

Q: 10 Convert the Cartesian equation 2 xy = 1 in polar equation form. r²cos2θ = 0 cosθsinθ = 1/2…

A:

Q: Write the equation (2² + y²)² = 10 xy in polar coordinates. a) Or? = 10 cos(2 0) b) Or? = 10 sin(0)…

A: We know that For conversion to polar form from cartesian equation. x=rcosθ y=rsinθ  Put these values…

Q: Replace the Cartesian equation x² + y² equation. OA) r sin² 0 = 4 cos 0 B) r = 4 sin 0 Oc) r = 4 cos…

A:

Q: Write in Polar form: *(cos e + z sin 8). i sin 0). (0 < 0 < 2n and round to 3 decimal places) - 17 +…

A: We have to find value of r and θ Consider ,z=-17+12iHere x=-17 and y=12 Here we will use the…

Q: Show that cos(18θ)=cos^3(6θ)−3cos(6θ)sin^2(6θ) and use this identity to find an equation in…

A:

Q: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) — 12 — Зі r =…

A: Given: -12-3i. The objective is to write the polar form.

Q: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) – 12 – 3i r = ,…

A:

Q: If z = r cos 0 + ir sin 0 then 1 / z has absolute value __ and angle __ . Its polar form is __ .…

A:

Q: snip

A: (a) z=3cos20°+isin20°w=5cos100°+isin100° Then we get,…

Q: Consider the polar equation defined by r= 5 cos(2 sin 6), where 0<0< 2x. Determine the missing…

A:

Q: 3. Justify your answer to part 2 by converting polar equation to rectangular equation. =2/sin 0 t /…

A:

Q: 1a) Convert the Cartesian equation (x^2 +y^2-1)^2 +4y^2-1 = 0 to polar coordinates. 1b) Use a…

A: By using the following substitution we can convert the Cartesian equation to polar form. x²+y²=r²…

Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

A: To determine : The coordinates of the point given in the picture in polar form based on the given…

Q: Find zw and Leave your answers in polar form. W Z = 2( cos 130° + i sin 130°) W = 4(cos 290° + i sin…

A: We will use the…

Q: 1) (a) Convert BOTH of the below equations from either polar to rectangular or rectangular to polar.…

A:

Q: 5. If z = 2(cos 25° +j sin 25°), find z in polar form.

A: It is simple calculation in polar form

Q: 5. Find the Cartesian form of the polar equation: r sin 0 = In(r cos 0)

A:

Q: 2. Express in true polar form, z 5(cos 55°-j sin 55°)

A:

Q: Find the equation of the tangent line to the polar curve r = 2 – sin(θ) at θ = π/3. Draw

A:

Q: 6. Find the area of one loop of the polar curve r = 2 sin 30

A:

Q: Graph the polar equation. r=-4 sin 0 Part: 0 / 2 Part 1 of 2 Plot six points satisfying the polar…

A:

Q: For the given rectangular equation, give its equivalent polar equation. 6x - y = 14 r= H 14 6 sin…

A:

Q: 9/2 9/2 2 Convert the point with Cartesian coordinates to polar coordinates. Enter exact values for…

A:

Q: Here are the problems for you to answer. Work on your solution carefully to arrive at the correct…

A: We will find out the required value.

Q: 6) Perform the indicated operations. Leave the resul in polar form. [50(cos 236° + j sin…

A: Given, 50cos236°+jsin236°2cos84°+jsin84°125cos47°+jsin47°

Q: Find zw and W Leave your answers in polar form. - TC TO Z= 6 cos + i sin 11 11 TO W = 6| cos COS + i…

A:

Q: 44. The furthest point from the pole to the polar curve r = 2+ V2 sin 0 occurs when 0 = A. в о C 2

A: Answer

Q: What type of polar curve does the equation r = 8 sin^2 (@/2) represent?

A:

Q: Express the given equation in polar coordinates. 16xy = 121 121 ? cos 0 sin 0 = 8 121 r² tan 0 = 16…

A:

Q: What is (x - 12)² + y² = 144 in polar form? r = 24 sin 0 r= 24 cos 0 O Option 1 r= -24 sin 0-144…

A:

Q: 4. a) Express the given rectangular equation in polar form. Solve for r or r2 if possible. x? = y? +…

A: Use x= rcostheta Y= r sin theta X2+y2=r2

Q: 5/3 Convert the point with Cartesian coordinates to polar coordinates. Enter exact values for r and…

A:

Q: Convert the rectangular equation 2x - 4y = 5 into polar form. 1 O r = 2 cos 0-4 sin 0 5 Or 2 sin 0-4…

A:

Q: Write in Polar form: r(cos 0 + i sin 0). (0 < 0 < 2n and round to 3 decimal places) 19 – 4i r = .0 =

A:

Q: Find the polar equation for the Cartesian curve ² Or 1 T= cos 2 1 Or=sin @tan 0 2 T = Or= Or T = 1 1…

A: The given cartesian curve x2=y2 we have to find the polar equation

Q: For the polar equation r = 4+ 2 sin 0 :

A: We have r=4+2sinθ A graph is symmetric about x-axis if rθ=r-θ A graph is symmetric about y-axis if…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.