Radius of curvature at any point on the curve x = a (0 + sin 0), y= a (l – cos 0) is (a) 2а сos (b) 4а сos 2. (c) a cos – (d) None of these

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A: Apply reduction formula:∫sinnx dx = n-1n∫sinn-2(x)dx - cosx. sinn-1(x)nwith n=4∫sin4x dx =…

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A: We use the product rule

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A: Given, y=sin(3x) ∴ Frequency in radians, ω=3 ∴ Frequency in Hz, f = ω2π => f = 32π Time period, T…

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Q: Prove the following trigonometric identities. 1 cotx a) 6 cosx| 6 cosx = 6sin² x COSX CSCX

A: The details solution is given below

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A: Solution: Let the given integral is I=∫sin6cot4e-4xcos4cot4e-4xdxe4xsin24e-4x ......(1) Substitute…

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A: We need to find tangent, normal, binormal vectors.

Q: (6) Find дл ду : ye+sin(2)=423 (8 points)

A: Explanation is given below:Explanation:

Q: Q# (13 Rewrite: cos (x)sin(x)dx A) ſ u'du 1/2 B) Tu°du V312 C) [ -u°du 1 V3/2 D) [ u°du 1 V3/2 E)…

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Q: V. Find the third derivative: 1) y = 10 tan(x) - 2 cot(x) 2) y = x³ - x² sin (x) 1 3) y = 2 sin(x)-4…

A: The given problem is to find the 3rd derivative of the given functions.

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A: Here, the angle is Here, given that,

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A: Solution:

Q: 6. (5 points) Suppose sin e = - 2 and e is in Quadrant 4. What is sec 0? 5 /29 V21 V (a) (e) 2 5 (a)…

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Q: 5) e*. 5*

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Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

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Q: 3) Find the Frenet (TNB) frame for the function at the point (2, 5n,0). Hint: once you find T and N,…

A: Given that  r(t)=-2cos3t,5t,2sin3t The formula for T is, T=r'r', Take the derivative for r,…

Q: If y=cos (3x+5 ) then the derivative is - 3 sin(/3x+5) 2/3x+5 b) y'=-3sin(/3x+5) V3x+5 a) y'=- c)…

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