Find the angle 0 between and 37 such that sec(0) = – /2. -

Q: Plot along with its tangent r = -6ecos0 + 8 cos 40 in %3D 4

A: We knowx = rcosθy = rsinθGiven: r = -6ecosθ+8cos4θ                     Where θ∈0,2π     Hence, x =…

Q: The curves 71(t) = (2t, t°, – t) and 72(t) = (sin(3t), sin(2t), t – 7) intersect at the origin. Find…

A: Given : The curves r1(t)→=2t,t6,-t2   and  r2(t)→=sin(3t),sin (2t),t-π intersect at origin(0,0,0).

Q: Find sin u and cos u if the terminal side of u lies along the line y =- 2x inquadrant II.

A: Given: Line y=-2x in quadrant II. Note: 1] sinu is positive in quadrant II 2] cosu is negative in…

Q: 5. Find the values of a and b such that dx tan 1 + sinx a + b . %3D

A: We need to integrate ∫11+sinxdx

Q: The curves 71(t) = (5t, t°, - 4t) and 72(t) = (sin(t), sin(3t), t – ) intersect at the origin. Find…

A:

Q: Find all the points of intersection of the curves r=cos3θ and r=sin3θ.

A:

Q: Find the length of the curve r = 4 cos 0

A: Given curve is r=4cosθ We have to find the length of the given curve. The length of the curve in…

Q: Find the length of the curve over the given interval. r = 4 sin θ, [0, π]

A:

Q: If rcos(x)sin(y)=a, rcos(x)cos(y)=b and rsin(x)=c, find r.

A: Formula used is written in the bracket of the first photo.

Q: Find the circumference of the curves x=e^-2θ (sinθ+cosθ), y=e^-2θ (sinθ-cosθ) over the interval 0 ≤…

A: To find: The circumference of the given curves. Given information: Concept used: If a functions are…

Q: Q4) The standard formula for the tangent of the sum of two angles is tan x + tan y tan(x +y) 1- tan…

A:

Q: The circles r = (3)^1/2 cos u and r = sin u intersect at the point (((3)^1/2)/2, pi/3) . Show that…

A: We have given circles equation r=3cosu and r=sinu For intersection point of these circles…

Q: 01: Find the angle () between the tangents lines of the 3 sec 0 and the cardioid r 4(1+ cos 0) at…

A:

Q: The curves 7₁(t) = (– 2t, t³, tº) and 7₂(t) = (sin( – 2t), sin( – 4t), t – π) intersect at the…

A: Here, the given curves are: r→1(t)=-2t,t5,t6 and r2→(t)=sin(-2t),sin(-4t),t-π which intersect at the…

Q: Find the exact length of the curve r = sin 0 + cos 0.

A:

Q: express sin(x+y+z) in terms of cosine and sines of x, y and z

A: Answer and explanation is given below..

Q: 01: Find the angle () between the tangents lines of the 4(1 + cos 0) at the line r 3 sec 0 and the…

A:

Q: Find the length of the arc of x²+y²=64 from x=-1 to x=-3, in the second quadrant.

A: Given curve: x2+y2=64

Q: Sketch the curve corresponding to r = 1 + cos θ.

A: we have to sketch the graph of the polar curve r=1+cos θ.

Q: Find the exact length of r = 3 sin 0 + 4 cos 0. II

A:

Q: Find the length of the curve r= 1+ sin(20) Oses- /20

A:

Q: Write the equation of the line tangent to the graph of r : 4 cos 0 when 0 = ". %3D %3D

A:

Q: Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

A: given : formula for arc length is as below :

Q: Find the angle between the radius vector to the curve r = 2a sin 3u and its tangent when u = pai/6.

A:

Q: The curves r₁(t) = (5t, t², t3) and r₂(t) = (sin(t), sin(5t), 4t) intersect at the origin. Find…

A: see my solution below

Q: 01: Find the angle (y) between the tangents lines of the line r = 3 sec 0 and the cardioid r = 4(1 +…

A: Solution is given below:

Q: Find the length of one arch of the cycloid = 5(t-sin(t)),y- 5(1-cos(t)).

A:

Q: The curves r1(t) = (3t, t2, t) and r2(t) = (sin(t), sin(5t), 5t) intersect at the origin. Find their…

A:

Q: What angle does the tangent to the curve y(x) = sin² (x/9) + 13sin(x/9) at x = 9n make with the…

A:

Q: Find the length of the curve y=In (cos x), -≤x≤0. The length of the curve is. (Type an exact…

A:

Q: Find a numerical approximation to the length of c(t) = (cos(4t), sin(8 Use decimal notation. Give…

A: Given

Q: Find the length of the curve r = 4 – 4 sin 0

A:

Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t) - sin(9r), Ostsn 9 cos (47)…

A:

Q: Mutiply    (cos theta  +3 )2

A: We have to find: (cos theta  +3 )2

Q: Find the are of the sector on the specified interval  r= sqrt*tan theta  0 less than equal to theta…

A: Find the area

Q: The sine of the acute angle between the plane n and the line /, where n: x- y+z= 2, and x-2 = y+1 -…

A:

Q: 1. If ß be the angle between the lines of regression, show that tan B = (1 -) 0,0/r (o, + o,).…

A:

Q: Mutiply    (sin theta + 4) (sin theta +3)

A: Trigonometry: (sin θ+4)(sin θ+3) We need to multiply the above factors.

Q: Find the concevity. point of infleetion, of fluj n=770 Also explain it jeometrically

A:

Q: 5. Find the length of one arch of the cycloid x = sin and y = 1- cos 0

A:

Q: Find the cosine of the angle between the curves (cost, -sin(t)/5, sint) and (cos(nt/3), sin(nt/3),…

A:

Q: Find the angle in radians between the planes -2x + z = 1 and -ly+ z = 1.

A: See the answer below

Q: cos ydy Sin y+ 5 sin 3 sin y+6

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: The curves r1(t) = (- t, t°, 2t°) and r2(t) = (sin( – 4t), sin(5t), t – n) intersect at the origin.…

A: Given: The curves,  r1→(t) = -t, t5, 2t3  and  r2→t = sin-4t, sin5t, t-π intersects at the origin.…

Q: divide the line segments (4, 14) and (8,8)into a ratio of 2:1: 3 36 30 sin f(x)

A:

Q: At what points does the curve 2a cos t - a cos 2t, y = 2a sin t – a sin 2t x = ave vertical or…

A:

Q: An object moves such that its velocity in meters per second is given by v(t) = cos t. What is its…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.