How does y= sin x compare to y= cos x in terms of transformation (explain) convert • f(x) = Cos [2(x-π/2)] and f(x) = Cos (3x) To g(x) = Sin [b(x-h)] + k

Q: d -1 ) Prove that cos 1(x) : dx V1-1

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Q: r sinx Evaluate: (2x-)(1+cos'r

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Q: / [sec-(x) – csc (x) ]dx Evaluate: A cot(x) + tan(x) +C (B ®esc (x) +sec (x) +C C) © jsec (x) – csc…

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Q: Prove that sin(x + y) sin(x − y) = sin²x − sin²y. -

A: Formula's

Q: f(x) = -2sin(x) Amplitude: f(x) = -3cos(x) Amplitude: f(x) = 6sin(x) f(x) = 10cos(x) %3D Amplitude:…

A: If f(x) = Asin(mt + n) or f(x) = Acos(mt + n) then amplitude = |A|

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A: To evaluate the double integral, first find the integral with respect to x by substitution method.…

Q: Let f(x) = sin2x and g(x) = cos2x. Determine whether h(x) is in span(j(x), g(x) ) h(x) = cos 2x

A: Given  f(x) = sin2x, g(x) = cos2x and h(x) = cos2x Then, we have to determine h(x) is in span(f(x),…

Q: Suppose S (x) =sin(3x – 2). Evaluate: /f(x) dr A - 3cos(3x – 2) + C (A) (B ® --cos(3r – 2) + C ©…

A: Given, f(x) = sin3x-2To evaluate:∫f(x) dx This can be done as follows:

Q: Determine if the setsin² {sin²x, 1-cos(2x)} is linearly dependent or linearly independent on I =…

A: Let B={sin2x,1-cos(2x)}.

Q: (a) y = In(sec²x) (b) y ecos + cos(e) x² −1+2 (c) y = x (d) y = sin² (e) y = (f) y = (cos(√sin(x)))…

A: Let's consider  the properties of differentiation.Let f(x) and g(x) are two different function…

Q: If f(x) = sin x, show that f(x + h) – f(x) = sin x cos h – 1 sin h + cos X h h

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Q: Evaluate sec³ (0) tan³ (0)dē. ○ sec (0) - sec³ (0) + C ○ sec³ (0) + sec³ (0) + C O sec³ (0) + sec(0)…

A: Step 1:To solve the integral ∫sec5(θ)tan3(θ)dθ, we can use substitution and trigonometric…

Q: sin(x) + cos(y) 1 + sin(x) cos(y).

A: Given query is to find the dy/dx at x = 0 and y = π/2

Q: -1 +tan (x), then

A: Trigonometry: y=cot-1(1x2)+tan-1(x2)y=tan-1(x2)+tan-1(x2)y=2tan-1(x2)

Q: -1 Let f(x) = (3 sin z + 4 cos z)tan f'(x) = %3D

A: Given  f(x)=(3sinx+4cosx)tan-1xTo find f'(x):

Q: Prove the identity. Work on one side only. cos(4x) = 18 sin² x+8 sin ¹ x

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Q: Deseribe the transformations applied to y = sin x to obtain y = 2 sin(3x+5) + 1- %3D

A: y = sinx ---> y = 2 sinx,  The graph is stretched along y axis by a factor of 2   y = 2 sinx…

Q: (x²-1) (*+3x +)[tan (1늦)그 dx

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Q: Evaluate: f(cos 5x - 2 sin 3x) dx O sin 5x - cos 3x + C Osin 5x - cos 3x + C O sin 5x+cos 3x + C…

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Q: Differentiate the functions. a) f(x) = 1– 2x +*

A: Given problem is  :

Q: Derive y: x+, y = (sin((x² – x)*))x²+x %3D

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Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + cosx c) f(x) = d) f(x) = (5 – x²)· e*

A: Suppose f and g are differentiable function .Then note the following results : The power rule of…