Graph the "Double Folium", r = 4 cos sin 0. Graph the "Lemniscate of Bernoulli”, 12...
convert to radians
5) γ 4cos (2θ-5) r 3 (sin(e - 2))2 + 4 cos(20-5) r-6(sin(9-2))2 + 4 cos(2e-5) 9(sin(9-2))2 + 4 cos(2e-5) r 12(sin(e - 2))2 +4 cos(20 5)
5) γ 4cos (2θ-5) r 3 (sin(e - 2))2 + 4 cos(20-5) r-6(sin(9-2))2 + 4 cos(2e-5) 9(sin(9-2))2 + 4 cos(2e-5) r 12(sin(e - 2))2 +4 cos(20 5)
A curve called the folium of Descartes can be represented by the parametric equations shown below. 912 1 + 13 9t and y 1 + t3 (a) Convert the parametric equations to polar form. 9 cos( 0)sin (6) c())3 (sin(0)5 cos(θ) ),+ (sin( (b) Sketch the graph of the polar equation from part (a). 71/2 0.10 0.05 -4 0.05 0.10 0.15 -0.05 0.05 π/2 10 1.0 0.5 0.5 -0.5 10 -0.5 (c) Use a graphing utility to approximate the area...
please solve it with polor coodinate graph
4. Find the area. a. Inside one leaf of the three-leaved rose cos30 r= b. Shared by the circle r 2 and the cardioid r 2(1+sin 0) c. Inside the circle r-3 cos 0 and outside the cardioid r=1 - cos0 d. Inside the circle r 4 sin0 and below the horizontal line r 3 csc e. Inside the outer loop of the limason r1-2 cos f. Inside the lemniscate 6 sin20 and...
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
Describe the graph of the polar equation. 7r cos 0 + r sin 0 = 5 O A. Line with slope - 7 and y-intercept (0,5) O B. Vertical line passing through (7,0) O C. Line with slope 5 and y-intercept (0,7) OD. Parabola with vertex (7,5) opening upward
Which of the following has the same graph as r= cos 120? Confirm your answer with algebra. 0 b.r-cos 12 a. r sin 120- T=sin 120 O r-cos 12 cOs 0 To confirm this answer, rewrite the equation in terms of cos 120 using the identity sin 0- Applying this identity gives
3. If T2 = r3 cos(0) sin(d) and v2 = sin(0) cos(O)f + r sin(0)θ + r2 sin(d)φ compute the following (a) ▽T, (b) ▽.
AME: 2. (24pts) Consider the curve given in polar coordinates by r-12 cos(0) Vsin(0), (0 0 < #). (i) Make a table of the values of the function f(0)--12 cos(0)/sin(0) /6 /4 n/3 5m/12 m/2 7m/12 2n/3 3n/4 5n/6 11 m/12 f(0) are to be rounded to two decimal places. (Hint. Given on 0, r); all the values f(0) an angle 9, enter the value of 0 to the variable C of your calculator, and then evaluate /(0) using the...
QUESTION 12 Use a double-angle or half-angle identity to find the exact value of: cos(0) = and 270° <=< 360°, find sin 5 OAV10 10 B. 10 C. None of these OD 10 3 17 OE 4 QUESTION 13 Use a double-angle or half-angle identity to find the exact value of: 3 sin(0)= and 0° <o<90° , find tan 5 - šar 10 OA. 3 B.V10 Octs OD. -V10 E V30 QUESTION 11 Use a double-angle or half-angle identity to...
Verify the identity. (6 cos 0 - 2 sin 0)2 + (2 cos 0 + 6 sin 0)2 = 40 Choose the sequence of steps below that verifies the identity. B. O A. (6 cos 0 - 2 sin 0)2 + (2 cos 6 + 6 sin 0)2 = 36 cos 20 - 12 cos 0 sin 0 + 4 sin 20 + 4 cos 20 + 12 cos 0 sin 0 + 36 sin 20 = 36 (cos_0+ sin...