By eliminating the parametert, find a Cartesian equation of the curve. Draw the curve and indicate with an arrow the direction in which the curve is traced as t increases. 1) tan² t, y = sect; -

Q: Given the parametric equation: x=cos(3t), y=sin(3t), 0 less than or equal to t less than or equal to…

A: Given: x=cos3t ,y=sin3t, 0 ≤ t ≤ π2

Q: hinormal of the curve traced by Q makes an angle tan- (cp/o V(c2 + o?)} with PQ.

A:

Q: Consider the following. tan2(0), y = sec(0), -n/2 < 0 < t/2 X = (a) Eliminate the parameter to find…

A:

Q: Consider the following. co) X = sin y = cos (a) Eliminate the parameter to find a Cartesian equation…

A: x=sinθ2 sinθ2=x θ2=arcsinx θ=2arcsinx

Q: Plot the curve r = 1+sin 8. Then find the length of the curve.

A:

Q: Find the lengths of the curves The parabolic segment r = 6/(1 + cos θ), 0 ≤ θ ≤ π/2

A:

Q: Consider the following. x = 7 sin(6?),    y = 7 cos(6?),    0 ≤ ? ≤ pi/3 (a) Eliminate the parameter…

A:

Q: Eliminate the parameter t from the following. x = 3 + sin t, y = 5 + cos t Sketch the graph of the…

A:

Q: *6. In the figure, the larger circle, centre O, intersects the smaller circle at P and R. Q is…

A: Given that the larger circle with center O, intersects the smaller circle at P and R. So, OP, OR are…

Q: In the following sketch, O is the centre of the larger circle, and a point on the circumference of…

A:

Q: Show that cos 120 cos 40 – 3 cos 40 sin? 40 and use this identity to find an equation in rectangular…

A: We have to show that cos12θ=cos34θ−3cos4θsin24θ Consider  cos12θ=cos34θ=cos3P        Let P=4θ We…

Q: Three observation towers p, q and r are such that p is 3km on a bearing of 40° from q. r is 9km due…

A:

Q: Sketch the curve and Find the length if the curve: x=cos(2t), y=sin(2t), 0<_t<_ pi/2

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve, and sketch the curve and indicate…

A:

Q: Given the curves r1 = 1 + 3 cos(θ), 0 ≤ θ ≤ 2π, and r2 = 3sin(2θ), 0 ≤ θ ≤ 2π a.   Plot both curves…

A:

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

A:

Q: Consider the following. X = sin A y = cos -π<θ< π (a) Eliminate the parameter to find a Cartesian…

A: To determine the Cartesian equation of the given curve.

Q: Show that the graph of the equation r=2a cos θ,a&gt;0, is a circle of radius a with center at (0,a)…

A: Given: r=2a cos θa&gt;0

Q: A simple curve is shown below. Given: A and T (tangent distance) Required a.) E b.) M c.) Length of…

A: A simple curve is given. Given - Deflection angle=∆Length of tangent =T To find - (a) EE is length…

Q: Find the length of the curve. The curve r= 8,/1+ sin(20), 0 <0< 4 A) 27 C) 8(7+ In(m

A:

Q: Use the arc length formula to find the length of the curve y = 3x - 1, -1 s xs 3. Check your answer…

A:

Q: Show that r = a cos θ + b sin θ is the equation of a circle passing through the origin. Express the…

A:

Q: 1. Show using similar triangles that tan 0 and cot 0 are the respective measures of line segments AR…

A: Using figure ,∠QOA + ∠QOB = 90°⇒θ+∠QOB = 90°⇒∠QOB = 90°-θIn ∆QBO ,∠QBO = 90° and ∠QOB=90°-θ ⇒∠OQB =…

Q: From the information given, find the quadrant in which the terminal point determined by t lies.…

A:

Q: Sketch the curve r= cos 20

A: Let us make a table for the given function θ 0 π/4 π/2 3π/4 π 5π/4 3π/2 7π/4 2π r 1 0 -1 0 1 0…

Q: Consider the following. x = tan2(0), y = sec(0), - T/2 < 0 < T/2 (a) Eliminate the parameter to find…

A: Explained below

Q: Consider the following. x = 4 sin(80), y = 4 cos(80), 0sos (a) Eliminate the parameter to find a…

A: Solution: x=4 sin (8θ)y=4 cos(8θ)  ,     0≤θ≤π4 Let 8θ =t  So,   0≤θ≤π4 multiplying by 80≤8θ≤8π4…

Q: Photo attached

A: Given,

Q: Sketch the following curves and find the points of intersection of the pairs of curves. a) r=…

A:

Q: The curves with equations x  =a sin nt , y = b cos t are called Lissajous figures. Investigate how…

A: Given, Lissajous figures x = a sin(nt) and y = b cos(t) We have to investigate how the curve varies…

Q: Consider the following. X = 7 cos(0), y = 8 sin(0), - T/2 < 0 S TT/2 (a) Eliminate the parameter to…

A:

Q: Consider the following. x = 3 cos(θ),    y = 4 sin(θ),    −π/2 ≤ θ ≤ π/2 (a) Eliminate the…

A: Calculation:(a)Compute the Cartesian equation as follows.Rewrite the equation x = 3cos(θ)  and y =…

Q: The circles r (V3/2, 7/3). Show that their tangents are perpendicular there. V3 cos 0 and r = sin 0…

A:

Q: A In cach circle 0, OP is a radius and PT is a tangent segment. Solve for the missing side of the…

A:

Q: Which one of the following points lies on the curver = sin 0 – 5. %3D TT o (-5, n) o (5, 0) (5, 2)

A: Put all points on curve, point which satisfy the equation , lie on curve.

Q: Find the length of the curve over the given interval: r=3acos(theta) Interval: [-pi/6,pi/6]

A:

Q: If the parametric curve starts at (- 2, – 9) when t = 0 and ends at (5, 7) att = 1, then find a, b,…

A:

Q: Consider the following. x = sin(0.5θ),    y = cos (0.5θ),    −π ≤ θ ≤ π (a) Eliminate the parameter…

A:

Q: If the parametric curve starts at (5, 10) when t = 0 and ends at (3, 8) at t = 1, then find a, b, c,…

A:

Q: Eliminate the parameter t from the following. x = 2 sec t, y = 2 tan t   Sketch the graph of the…

A: Given,           x=2sect and y=2tant

Q: Consider the following. X = sin y = = COS (a) Eliminate the parameter to find a Cartesian equation…

A:

Q: Given x= sin 0, y = cos 0, n <o< 2n a) eliminate the parameter to find the rectangular equation of…

A:

Q: What symmetries do these curves have?? r² = 1 – sin 0

A:

Q: Find the Cartesian equation of the curve: x = 2cos(theta) y = 1 + sin(theta) where theta is…

A: Given that the equation of the curve, x=2cosθy=1+sinθWhere,  0≤θ&lt;π2

Q: Consider the following. x = tan?(0), y = sec(e), -1/2 < e < n/2 (a) Eliminate the parameter to find…

A: x=tan2(θ) and y=sec(θ) knowing that tan2(θ)=(tan(θ))2=sin2θcos2θ and that…

Q: Consider the following. x = sin(t), y = csc(t), 0<t< R/2 (a) Eliminate the parameter to find a…

A:

Q: Given that point T on the unit circle with center at (0, 0) has coordinates ( 4, 12 ), find the…

A:

Q: Determine the width of a petal of the curver = 2 cos(20) (The width is defined to be the videst part…

A: Given curve r = 2cos(2 theta) We have to find the width of a petal of the curve r = 2cos(2theta)

Q: Consider the following. x = 9 sin?(t), y = 9 cos?(t) (a) Eliminate the parameter to find a Cartesian…

A: