For an angle <0 < T, f ind 0 for sin( ) + csc( ) + cos ( ) = 3

Q: 1 Use the Trapezium Rule, with seven ordinates, to evaluate In(sin.r+3)dxcorrect to four decimal…

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Q: What is the Length of the arc of the circle r = sin θ that remains outside of the cardioid r = 1 —…

A: Arc lenght in polar curves: The formula to find the arc length is, Arc length=∫θ1θ2dxdθ2+dydθ2dθ…

Q: Find the length of the path over the given interval. (sin 3t, cos 3t), 0 ≤ t ≤ π

A: xt, yt=sin3t, cos3t,   0≤t≤π Here, xt=sin3t,  yt=cos3t Now differentiating with respect to t, we get…

Q: Find all angles between 0 and 2r satisfying the condition V3 sin x = Separate your answers with…

A: Given: sinx=32

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: In AXYZ with a right angle at Y, the cosine ratio can be used to find the length of XZ as O a) XY…

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Q: – sin x show that - In |sec x +c ??? %3D COS X

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Q: The circles r = sqrt(3) cos u and r = sin u intersect at the point (sqrt(3)/2, pai/3). Show that…

A: For r=sqrt(3)cos(theta) find dr/d theta

Q: Q4) The standard formula for the tangent of the sum of two angles is tan x + tan y tan(x +y) 1- tan…

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Q: Suppose sin u=x and u is between 0 and 2. What is cos u? V1- 22

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Q: Find the angle(s) that satisfy the given values in the interval (0, 2r) 1. cos I = 2. secz = V2 3.…

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Q: The circles r = (3)^1/2 cos u and r = sin u intersect at the point (((3)^1/2)/2, pi/3) . Show that…

A: We have given circles equation r=3cosu and r=sinu For intersection point of these circles…

Q: e Suppose flx) = Sin (x) For which value %3D of a, osas T, will f'la) = 0.

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Q: Find all angles between 0 and 2T satisfying the condition COS X = 2 Separate your answers with…

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Q: Calculate the length of the path over the given interval. (sin 4t, cos 4t), 0 <t <T

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Q: S sec" (0) tan" (0) do is u = tan(0)

A: Evaluate ∫sec10θ tan8θ dθ

Q: Find the length of the path over the given interval. (2 cost − cos 2t, 2 sin t − sin 2t), 0 ≤ t ≤…

A: x(t)=2 cost − cos 2t y(t)= 2 sin t − sin 2t interval- 0 ≤ t ≤ π/2

Q: Show that the curves r = a sin θ and r =  a cos θ intersectat right angles.

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Q: 01: Find the angle () between the tangents lines of the 4(1 + cos 0) at the line r 3 sec 0 and the…

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Q: 2. Give the values of the six circular functions of the standard angle 0 generated by an arc whose…

A: I have solved the question 2 for you as we can solve one question in one session. f you want the…

Q: If u = tan- the value of x2 +y? +xy du du at x = 1 and y = 3 is

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Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x – 4 sin°x .…

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Q: the solving for equa tion ty=o is 1-y= COSX %3D 2-y= Sin x %3D y= tax

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Q: If f cos xdx = A + B sin x + Csin²x+ Dsin³x+ E sin*x+ Fsin5x, what is the value of A + B + CD + E +…

A: Consider ∫cos5x dx =∫cos4x cos x dx =∫(cos2x)2 cos x dx=∫(1-sin2x)2cos x dx…

Q: 2. ind the length of an arc of the cycloid given by, x = a(0 + sin0), y = a(1 + cos0), Ar

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Q: If x = sin2 (u) and y = cos² (u), then dy is : dx а. 1 b. cot(x) C. tan(x) d. 1-

A: Differenriate

Q: By using u = tan 0, evaluate tan 0 sec*e de.

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Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

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Q: The area of the region that lies inside r = sin0 and outside r=1 cos60 is given by:

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Q: FIND SIN' A WHERE A= at b

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Q: Give an example to justify that sin (A + B) is not equal to sin A + sin B. Limit A and B to special…

A: Special angles are those angles at which the values of the trigonometric ratios are known. For…

Q: If  sin⁡x=e^y,  0<x<π, what is dydx in terms of  x?

A: Given sin x = ey   ..................(1) Differentiating both sides with respect to x  d(sinx) / dx…

Q: find area Inside the circle r = 4 cos 0 and to the right of the vertical line sec 0

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Q: Let P = {x € R | sin(x) = 0} and Q = {na | n E Z}. What is the relationship between P and Q?

A: Let P = {x ∈ R | sin(x)=0}, and Q = {nπ | n ∈ Z}. What is the relationship between P and Q​

Q: ) // Show that y + y = 0, given that y = 2 sin x + 3 cos.x

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Q: Given that (-) x sin-1 -1 = COS eya. dy in the terms of x and y. dx Find

A: Given: xsin−1⁡1y=cos−1⁡eyx Since, dsin-1xdx=11-x2 and dcos-1xdx=-11-x2

Q: 22. Determine Sz sin? y cos y dy

A: Given that: ∫0π2sin2ycos6ydy

Q: Given f(x,y) = e X cos y, Evaluate fx(0,2) cos 2 -sin 2

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Q: (2 cos t, 2 sin t, t), where 0 <t < .

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Q: Calculate the length of the path over the given interval. (sin 3t, cos 3t), 0 <t<+

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Q: Find fr(x, y) and f,(x, y) given f(r, y) = tan r - cos(r² – y³).

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Q: Find the points on the curve where the tangent is horizontal or vertical. Express the answer as…

A: Given, x = 4 cosθ, y = sin2θ

Q: Using a suitable substitution, (sin x cos“ x) dx can be 4 (A) - f u*du (B)

A: Given: ∫0π2sinxcos4xdx

Q: Given cos x sin x < 0; tan y = sec y < 0, find sin(x+y)

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Q: y = C, sin at + C2 cos at, (a not to be eliminated)

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Q: derivation is required

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Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x- 4 sin'x.…

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Q: Given, w=2iz - sin iz. Find i dz 2+ cos iz -2- cos iz -2+cos iz -2+cos z

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Q: If sin-r= In y, show that UTM dy (1-2) = y. dr

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