15. Restate r= 5 cos 0 in rectangular form.

Q: 1. Evaluate √2 √4x² dx using a trigonometric substitution.

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Q: Substitute cos 60 = u. Differentiate with respect to e on both sides. sin 60 de = du

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Q: • y = sin¬(10x) %3D

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Q: Verify that if y = ƒ(θ2 sin θ, then y'(θ) = ƒ'(θ) sin θ + ƒ(θ) cos θ.

A: We use the product rule

Q: Jo Jo L p sin o cos ddpd0do

A: convert rectangular co ordinate into spht coordinates  and put values

Q: 1+cosx ction x= Correct yo 3

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Q: 3- Represent in the form of x+ iy a) V8 (cos + i sin m) b) 6 (cos 7 + i sin7)

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Q: b) cos(-z)=?

A: In the question we have to find the angle of cosine which is lying in third quadrant as cosine is…

Q: So 3 3 cos y sin y dy

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Q: 11m If 0 = 6. then sin(0) • %3D cos(0) =

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Q: Let cos A = with A in QII and find V13 sin(2A) = Preview TI Enter your answer as a number (like…

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Q: So sin' z cos²z dr csc? z

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Q: If csc(z) = 6, for 90° <z< 180°, then %3D sin () %3D «(금) cos tan(플) - ||

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Q: 1, Solve for o 0-2T (a) sine 2 W cos 28 = 8- %3D O Zsin e- =o - omis ce)

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Q: Eliminate the parameter: I = sin 3t, y = cos 3t, 0 <t <T/3. = COS

A: x= sin 3t     and y=cos 3t     for    0≤t≤π3 We need to eliminate the parameter i.e. we have to…

Q: 1. Simplify (cos(4L25°) – tanh (0.3 + j0.7) cosh (In (3 + j5)(3+j5)) and write your final answer in…

A: Given expression is coshcos4∠25°-tanh0.3+j0.7ln3+j53+j5

Q: In right argle triargle, A =q0° and tanc = V3 End : sin B cośltcos Bsin C %3D

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

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Q: O do 5 sin cos de Sin ³0 + 3sing-4

A: Given that ∫5 sin θ cos θsin2θ + 3 sin θ-4dθ We can solve this by using substitution method. Needed…

Q: (a) sin(rxy) = x + y?

A: I am going to solve the given problem by using some simple caculus to get the required result.

Q: (Note: Check the answer by the calculator) sin 0 + In + 22+3 = -3 1-cos 20 In y? + 322- 4 = 2 2 +2ln…

A: Given system of equation can rewritten as : sinθ+ln1y+2z+3=-3lny2+32z-1-cos2θ2=421+cot2θ+2lny+2z=-3…

Q: I co cos (In x) dr

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Q: If (Mesin(2) dx = e°sin(2») + C, then the M is equal to

A: On solving this we will get

Q: sketch r= la 2 Sin'(o+)

A: Given r=1-2sin2θ+π3 Let us sketch the figure. Taken 0≤θ≤12π

Q: (a) (2 cos 8 – 3 sin 30) de dr CS Scannec with CamScanner

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Q: The value of So" 6 (4+ cos2x)dx is:

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Q: tanla= 2 with 3T LaL2p 3 2 and Sin lb) = 3 with IT L6LT 2. %3D

A: Solution:-  tana=-23   with 3π2&lt;a&lt;2π (fourth quadrant) sinb=34 with    π2&lt;b&lt;π   (second…

Q: Evaluating ³√9-x² dx using trigonometric substitution will lead to: 15/2 A cos²0d0 B 18 cos²0d0…

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Q: 5 1. If sec a with a in quadrant Il and cos B = with B in quadrant IV evaluate: 3 a) sin(a- B) b)…

A: If sec α=-52 with α in quadrant II and cos β=13 with β in quadrant IV, then to evaluate the…

Q: 2. Show that y = ce sin

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Q: b) SE cos(3x) sin(3x) 18

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Q: 57 then If 0 = sin(0) = %3D cos(0) = %3D

A: Given θ=5π6

Q: 6. Show 1 – 8sin?0 · cos²0 = cos(40) 10 pts

A: To show that LHS=RHS

Q: 2 Convert r = to rectangular form. 7 sin 0 COS

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Q: sketch r= la 2 Sin'co+)

A: r=1-2sin2(θ+π3)

Q: Se sin 4m Cos 4mdm (3)

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Q: Show that ea?,2 cos bx da = (VT /2a). a > 0.

A: Given integral is∫0∞e-a2x2cosbxdx=π2ae-b24a2, a&gt;0The integral is derived as shown below

Q: 2 =, where 0 < A < , what is the value of cos 4? 2 18+6/5 6. 18+6/5 18–6/5 6. V18-6/5 6

A: Use,  Cos (A) = 2 cos^2(A/2) - 1

Q: If z = os0+ I sin 0 and y= cos Isin p, then show that %3D 2 cos(@-).

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Q: sin(2 – 3i) cos(3 – 2i)

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Q: Find the areas of the regions . 1. Inside one leaf of the four-leaved rose r = cos 2u 2. Inside one…

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Q: 97. One petal ofr = 3 cos 50 %3D

A: The given polar curve is r=3cos 5θ. Evaluate the roots of the function r=3cos 5θ as follows. r=03cos…

Q: Dut answers without proper justification may Evaluate (3x° +4 sin a +1) dx Jo

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Q: 24) y = Sin' 2x.Cos2x (ans

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Q: Tt/2 2 sin(2x) dx 4– cos(2x)

A: The solution is:

Q: 2 Arc cos (1- y=

A: Given,   y=2arccos1-x2+4x-x2.   It is differentiated as follows:…

Q: 87 cos e do %3D O 4

A: In this question we have to evaluate the Integration.

Q: Determine the period as requested. 5) Feriod of y 5 sin 4x A) 4 C)2 -1/2

A: In this question, we want to find the period of the given function.