#16. EXPRESS AS A TRIGONMETRIC FUNCTION OF ONE ANGLE cos 70° cos 53° + sin 70° sin 53° cos 17° b. cos 61° sin 82° – sin 61° cos 82° sin 21 с. sin 57° cos 4° + cos 57° sin 4° sin 61 a.

Q: Consider the parametric equation x = 13(cos(theta)+theta(sin(theta)),  y =…

A: To find the length of parametric curve on [0,9π/4]

Q: The intersection points between the curves r = 3. and r = are 1-cos e 1+cose

A: The given curves are, r=11-cosθ                      ........(1) r=31+cosθ…

Q: Consider the following parametric equation.  x = 18(cosθ + θsinθ) y = 18(sinθ - θcosθ) What is…

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Q: Find: a f cos r dr Hint: In b sin r = b sin r dr sin r sin r = (1 – cos² r)² sin .r, etc. cS sin r…

A: To Evaluate:

Q: If P(x,y) is the point on the unit circle corresponding to 0, then use the definition of the cosine…

A: Option D is correct See below the answer

Q: 4. Find the acute angle between the curves y = sin r and y = cos r (0 < r <) at their point of…

A: We find the point of intersection by setting them equal

Q: By approximately how much will f(x, y, z) = x cos(rz) – 4x – 3y sin(xz) + y - change if the point…

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Q: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

A: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

Q: find dr&gt;du.23. r = 4 - u2 sin u 24. r = u sin u + cos u25. r = sec u csc u 26. r = (1 + sec u)…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Plot r = 4 cos 0: 0° 30° 60° 90° 120° 150° 180° 210° 90° 120° 60° 150° 30° 180° 0° 210° 330° 240°…

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Q: Find the Lengeh fror the foclowing Curves Dr= I+ Cos9 D rel-coso |

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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: (b) Given that cos (t) Vos(21) sin' (t) Jos(2)" |cos(2t) dy Find for the parametric equation given…

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Q: Q1 Find all the points of intersections of the curves r = 1+cos0 and r=1+sin r-1+(8) r=1+1)

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Q: Graph the following vector fields

A: (a)known fact:

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 Sc F · dr for F = 3yi – (sin y)j on the curve counterclockwise around the unit circle C…

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Q: Show that cos(18θ)=cos^3(6θ)−3cos(6θ)sin^2(6θ) and use this identity to find an equation in…

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Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0< 0 <…

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Q: Evaluate S(cos?y – sin?y – csc 2y)dy O -sin 2y + In|csc 2y – cot 2y|| + C O sin 2y – In|csc 2y – cot…

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Q: Consider the curves:r = 4sin 0 and r = 2 sin(0) + 2cos (0).

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Q: Show that Y + y = 0_given that y=2 sin x + 3 cos X y"

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

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: Show that cos21θ=cos^3(7θ)−3cos7θsin^2(7θ )and use this identity to find an equation in rectangular…

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Q: (a) Under the substitution, sketch a right-angled triangle and show that () 1 t sin 2 and cos 2 V1+…

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Q: 1) (a) Convert the following equations from parametric to rectangular. State the domain and range of…

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Q: Consider the following parametric equation. = 5(cos 0 + 0 sin 0) y = 5(sin 0 – 0 cos 0)

A: Given,          The parametric equation are x=5cosθ+θsinθ and y=5sinθ-θcosθ.

Q: d the area of the surface generated by revolving the curve x =cos (2t), y = 7+ sin ( 2° - xis. .....…

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Q: Find ſo F · dr for F = 8yi – (sin y)j on the curve counterclockwise around the unit circle C…

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Q: Find the slope of the line tangent to the following polar curve at the given point. 3π r= 5-5 sin 0;…

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Q: 6. Find the slope of the tangent line to the polar curve r = 2 cos 0 when 0 %3D You may use sin ,…

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Q: Find the slope of the line tangent to the following polar curve at the given point.   r=4−4sinθ​;…

A: Given a curve in polar form. We need to find the slope of the tangent line at a given point and also…

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

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Q: Consider the following parametric equation.  x = 14(cosθ + θsinθ) y = 14(sinθ - θcosθ) What is…

A: Given parametric equations are x=14cosθ+θsinθy=14sinθ-θcosθ

Q: 3. Consider the curves: r 4sin e and r = 2 sin(8) + 2cos (0). =

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Q: A fun ride for children follows the curve with equation Vi in x + 2 +2, 0 sxs 24, where y is the…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

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: Q8:- Find the intersection points between the given curves. r= cose 1- r= sin0 2- r= 3cos0, r=1+…

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Q: . Consider the function f(x) = cos(0.6z). %3D i. For the argument of cosine, 0.67. to vary by 2T,…

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Q: ch, choose its equation from the following. = sec (x+²) = y = cot (x + ²) 4 v=2 tan x 2 y=-csc x 1 T…

A: we have to find the graph

Q: The mass M of the Sun is approximately 1.989 × 10º kg, and the mass m of the Earth is approximately…

A: Let W be the work done by the gravitational force of the Sun on the earth from perihelion to…

Q: e cos (r) dr = (cos (r) + sin (r)) + C. COS COS %3D 2

A:

Q: The parametric equations for the paths of two projectiles are given. At what rate is the distance…

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Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Differentiate x with respect t. dxdt=ddtcos2t=-2sin t cost  Differentiate y with respect to t.…

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: 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: How did he get the value inside the circle by ===//= √xlt) sin (nwot) dit bn cl 11 2 (= (₁-7) Sin…

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Q: F- dr in the case when F(z,y) = (7y -sin (y) + 8) i+ (72 - cos (y))jis conservative, and Ais the…

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Q: jw F(w). 2 - TAN [* - ACOS(WT)] acos Tjw jw F(W) = -2A (₁ - cos (WT)). Tjw jWF(W) = -2A (asin" (WI))…

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.