The parametric equations of a curve are i. Show that dy/dx = sin t. ii. Hence show
Question:
The parametric equations of a curve are
i. Show that dy/dx = sin t.
ii. Hence show that the equation of the tangent to the curve at the point with parameter t is y = x sin t − tan t.
Transcribed Image Text:
X=
1
[, y =
cos³ t'
tan³ t, where 0
X=
1
[, y =
cos³ t'
tan³ t, where 0
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (8 reviews)
i To find dydx we use the formula dydt dxdt First we find dydt y tan3 t dydt 3tan2 t sec2 t 3tan2 t1 ...View the full answer
Answered By
Darwin Romero
I use a hands-on technique and am approachable to my students. I incorporate fun into my lessons when possible. And while my easy-going style is suitable for many subjects and grades, I am also able to adapt my style to the needs of the student. I can describe myself as friendly, enthusiastic and respectful. As a teacher, we can easily get respect from the students if they would feel respected first
0.00
0 Reviews
10+ Question Solved
Related Book For
Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook
ISBN: 9781108407199
1st Edition
Authors: Sue Pemberton, Julianne Hughes, Julian Gilbey
Question Posted:
Students also viewed these Mathematics questions
-
1. In the investigation you used the parametric equations for a circle, x = 3cos t and y = 3 sin t, to graph other geometric shapes on your calculator. Mathematically, do you think it is correct to...
-
Develop the parametric equations of a hyperbola by following these steps. a. Write the equation of a unit hyperbola in standard form using x and y. b. Replace x with 1 / cos t and solve for y in...
-
The parametric equations of a curve are x = e 3t , y = t 2 e t + 3. i. Show that y = dy/dx = t(t + 2)/3e 2t ii. Show that the tangent to the curve at the point (1, 3) is parallel to the x-axis. iii....
-
Elaborate the basic functioning of a hydraulic lift. Include the terms pressure, density, and buoyant force in the explanation. Give one example of a hydraulic lift you have encountered.
-
Check the requirements for regression for the data set of the TSX and the DJI described in Exercise 8.Is this data set a random sample?
-
What type of signal is the output of a non-ICP accelerometer?
-
The bar is made from a 2014-T6 aluminum alloy. Determine its thickness \(b\) if its width is \(1.5 b\). Assume that it is fixed connected at its ends. b 800 lb 5 ft 800 lb 1.5b
-
Kingsley Products, Ltd., is using a model 400 shaping machine to make one of its products. The company is expecting to have a large increase in demand for the product and is anxious to expand its...
-
Consider the following independent situations for an audit for the year ended 30 June 2020: 1. Freddy Ltd.'s accounts receivable agrees to its sub-ledger, but there is no aging review of the...
-
Sketch the graphs of the following functions. f(x) = -x 3
-
Outline a method for locating the relative extreme points of a function.
-
Identify and analyze each of the following transactions of Wolverine Corporation. The company uses the periodic system. March 3: Purchased merchandise from Spartan Corp. for $2,500 with terms of...
-
A 485-nm light beam passes through a slit and forms a diffraction pattern on a screen \(0.320 \mathrm{~m}\) from the slit. The \(n=1\) and \(n=-1\) dark fringes are \(22.4 \mathrm{~mm}\) apart on the...
-
A slit \(0.002470 \mathrm{~mm}\) wide is used to study a light ray made up of two wavelengths, \(482.0 \mathrm{~nm}\) and \(517.3 \mathrm{~nm}\), and the diffraction pattern is viewed on a screen...
-
As a financial manager it is often helpful to know the yield to maturity of outstanding bonds. Based on the information provided at MFL, use a spreadsheet to compute the yield to maturity for a bond.
-
You are doing x-ray diffraction on a crystal that has a cubic structure, using \(0.500-\mathrm{nm} x\) rays. If the lattice spacing is \(d=6.70 \times 10^{-10} \mathrm{~m}\), what are the two...
-
A monochromatic \(x\)-ray beam that has a wavelength of \(1.000 \times 10^{-10} \mathrm{~m}\) strikes a sodium chloride crystal that has a lattice spacing of \(2.815 \times 10^{-10} \mathrm{~m}\)....
-
A ball is released at the left end of these different tracks. The tracks are bent from equal-length pieces of channel iron. a. From fastest to slowest, rank the speed of the ball at the right end of...
-
Identify the source of funds within Micro Credit? How does this differ from traditional sources of financing? What internal and external governance mechanisms are in place in Micro Credit?
-
A geometric progression has first term a and common ratio r. The sum of the first three terms is 3.92 and the sum to infinity is 5. Find the value of a and the value of r.
-
The first four terms, in ascending powers of x, in the expansion of (1 + ax + bx 2 ) 7 are 1 14x + 91x 2 + px 3 . Find the values of a, b and p.
-
The function f is such that f(x) = 2 sin 2 x 3cos 2 x for 0 x . i. Express f(x) in the form a + b cos 2 x, stating the values of a and b. ii. State the greatest and least values of f(x). iii....
-
A couple obtained a $20,000 mortgage loan at an interest rate of 10.5% compounded monthly. (Original principal equals to PV of all payments discounted at the interest rate on the loan contract) (1)...
-
What strategies and tactics are employed to manage strategic risks and uncertainties, including geopolitical instability, supply chain disruptions, and emerging competitive threats, while preserving...
-
How do strategic planners integrate ethical considerations and sustainability imperatives into strategic planning processes, balancing short-term financial objectives with long-term societal and...
Study smarter with the SolutionInn App