Concept explainers
For the following exercises, the cylindrical coordinates of a point are given. Find its associated spherical coordinates, with the measure of the angle
405.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Calculus Volume 3
Additional Math Textbook Solutions
Thinking Mathematically (6th Edition)
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Thinking Mathematically (7th Edition)
Mathematics All Around (6th Edition)
Probability and Statistics for Engineers and Scientists
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
- Convert from cylindrical to rectangular coordinates. (0, π/5, 1/2)arrow_forwardFind the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = 6t'i + 21°j - 31°k 1sts3 6. 2 The curve's unit tangent vector is i+ j+ k. 7 (Type an integer or a simplified fraction.) The length of the indicated portion of the curve is 49 units. (Simplify your answer.)arrow_forwardChange the following rectangular coordinates to spherical coordinates (1, 1, -2√/2).arrow_forward
- For this homework problem remember to use spherical coordinates.arrow_forwardDetermine the moment of Inertia about the Y axis for the sections shown below. 20cm 5cm 15cm 5cm 5cm 30 cm Fig 1arrow_forwardTranslate the spherical equation below into both cylindrical and rectangular coordinates. Equation: tan2(φ) = 1arrow_forward
- (b) Convert from Cartesian coordinates to spherical coordinates. Give exact answers (no decimals), with positive angles in radians. (x, y, z) = (-4,0,-4√3)arrow_forwardr2 = 16 sin 2θ.Test for symmetry with respect to:a. the polar axis. b. the line θ =π/2. c. the pole.arrow_forwardConvert the given point to the indicated coordinate system. Spherical (?, theta, phi) = (3, (4/3)pi, pi/3)i. Rectangular (x, y, z)ii. Cylindrical (r, theta, z)arrow_forward
- A frog is sitting on the edge of a playground carousel with radius 1 meter. The ray through the frog's position and the center of the carousel makes an angle of measure e with the horizontal, and his starting coordinates are approximately (0.81, 0.59). Find his new coordinates after the carousel rotates by each of the following amounts. a. 2 z*+ y* = 1 C. d. (0.81,0.59) 2 е. - f. 2 g. T- 20 h. -20 b.arrow_forwardFind the position vector 7(t), velocity vector v (t),acceleration a (t), and the speed for z = t. 8. the motion of a particle described with parametric equations: x = 2 cos(2t), y = 2 sin(2t), Find the distance that the particle travels from t = 0, to t = 2.arrow_forwardy = xtan0 0 Given: height of shag = 7'1"= 7.083 Vo = 35 ft/s = 39.25 2 g = 32 ft/s ² 1 If 7'1"Shaquille O'Neal is at the free throw line (that is 4 feet from the point under the 10-ft rim of the basket,) and he throws the ball with the initial velocity 35 feet per second and the angle of inclination 0 = 39.25°, does he make the free throw successfully? Explain your answer in details. (Hint 7'1"=7.083ft and g = 32ft/s²) O 9x² 2v2cos²0 -4- + Yo 1 4' y = x tan- gx² 2 T 10 = 4 +an 39.25 - 16(4)² +7.083 10 22 10' 10 4 tan 39.25-162 | 13 , туо 2 2 Vo²cos ²0 2 (35) ² cos 39.25² +7.083 (35)² (cos 39.25)² solve in degrees for calculator NOT RADIANSarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,