1° = 2 + 3+ 4 + J6. 2 Prove cot 7- %3D

Q: B)Prove (cose + i sine)" = cosne + i sin ne

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Q: 2cos'z = COS T Select all correct solutions.

A: Follow the procedure given below.

Q: Find all solutions to the equation on the interval 0, 27): cos V3 2 T 47 3' 3 47 57 3' 3 * 27 47 5T…

A: Equation

Q: Express the number -5 in the form R(cos(0) + i sin(0)) = Reil where R>0 and 0 <0 < 2T.

A: rewrite -5 as -5=-5+0i comparing with z=a+bi a=-5 , b=0 R=a2+b2=-52+02=25+0=25=5 now…

Q: The curves 71(t) = ( – 5t, tº, t“) and 72(t) (sin(5t), sin(2t), t) intersect at the origin. Find the…

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Q: In Exercises 17–20, find dr/d0. 17. r = 4 – 0² sin 0 19. r = sec 0 csc 0 In Exercises 21–24 find…

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Q: Express the number –2 in the form R(cos(0) + i sin(0)) = Re where R> 0 and 0 ≤ 0 ≤ 2π. NOTE: Enter…

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Q: Convert r = 6(sin(0) + cos(0)) to an equation in rectangular coordinates in terms of x and y.

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Q: Express the number 2/3 – 3i in the form R(cos(0) +i sin(0)) = Re", where R> 0 and -7 < 0 <T. NOTE:…

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Q: If x = 4 sin 0, then J csc2ede = %3D

A: Here, ⇒x=4sinθ⇒sinθ=x4 By using Pythagoras theorem, We will have remaining side of the triangle…

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: Solve the cofunction of sec(3pi/10)

A: The given expression is sec3π10. Cofunction identities in radians. sec3π10= csc(π2 -…

Q: If cos A with A in QIV , find sec %3D a. sec | b. sec 2. с. sec A d. sec 4-5 %3D A sec e. A2 1/2 II…

A: Since you are asking multiple questions. We are answering only the first question. Given, cosA=18…

Q: theerem 3 2tt sine = S. I = do; a>l. anse 2T (a- Ja?) %3D a+ CEsO

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Q: 1 dt sin? tv1 – 9 cot² t sin²

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Q: Find a rectangular form of the equation. r(7 cos 0 + sin 0) = 4

A: To convert a polar form to rectangular form the following formulae are used.

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: B)Prove (cose + i sine)" = cosno + i sin no

A:

Q: 2.)S csc-³«(cosa)³da

A: Given ∫csc-3 α (cosα)3dαTo evaluate the integral:

Q: Express 1+ cos a + i sin a in the modulus amplitude form.

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Q: Express the number 5/3 – 5i in the form R(cos(0)+ i sin(0)) = Rei where R> 0 and -T <0 <T. NOTE:…

A: Given:     A complex number z:=53-5i. To Find:  The Polar form of z. i.e., z=Reiθ=Rcosθ+isinθ, where…

Q: and 0 e (5.0), find sece(0 – 5m). 3. If sin 0 =

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Q: Find the velocity, speed, and acceleration of 7(t) = ( cos(3t), sin(3t), t² + 2t ) CoS

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Q: Express the number –9 in the form R(cos(0) + i sin(0)) = Rei where R0 and 0 ≤ 0 ≤ 2π. NOTE: Enter…

A: Solution :  Given  number   - 9

Q: Express the number 7/3 – 7i in the form R(cos(0) + i sin(0)) = Re", where R>0 and -n < 0 < T. NOTE:…

A: Given complex number is 73-7i Let 73-7i=Rcosθ+isinθ                       . . . (1) where R&gt;0 and…

Q: a) Express 16sin 0 in the form a sin 0 + b sin 30 + c sin 50 , where a, b and c are constant.

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Q: Express the number 2/3 – 8i in the form R(cos(0)+ i sin(0)) = Reo, where R> 0 and -T <0 <T. NOTE:…

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Q: Find equation of r = 1 + 8 cos(0) in rectangular coordinates.

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Q: Convert r=1/1+sinθ to Cartisian

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

Q: Find the highest point on the cardioid r = 1+ cos 0.

A: We cal solve the problem by doing the derivative and set it to zero for finding theta.

Q: Find cos(u/2) if cosu=0.153 and u is in Quadrant-IV. round to the 4th decimal place cos(u/2)=

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Q: T Use Wallis' formula: sinº (1) cos² (1) dx

A: Follow the procedure given below.

Q: (3 cos t – 1)i + (2 sin t + 3)j,

A: We sketch the curve as

Q: %3D 20 24 tan 24 through solve this egni: Hint :oU=KL +2 =0 மு 3K²=Par ET %3D 2.

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Q: 7 Jlgull sin(2) = e-e- 2i eiz-e-iz 2 et +e-iz 2i e -e-i: 2i

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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: Graph the epitrochoid with equations x  =11 =cos t - 4 cos(11t/2), y = 11 sin t - 4 sin(11t /2)

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Q: x = 3 sin? 0, y = 2 cos? 0 in the given Cartesian form. y = (3-x)/2 with 0 < x < 3.

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Q: Express the number –5 in the form R(cos(0) + i sin(0)) = Re where R > 0 and 0 < 0 < 27. Reio NOTE:…

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Q: 2 If cos t : and t is in the 3rd quadrant, then cot t = 8 %3D V60 2 V60 8 2 V60 8 V60 O V50

A: Given:- cos(t) = -2/8  To find:- cot(t) in iii quadrant

Q: Express the number 3√3 - 6i in the form R(cos(0) + i sin(0)) = Re¹0, where R> 0 and -T≤ 0 ≤ T. NOTE:…

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Q: Find the length of the cardioid r = 1 – cos 0.

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Q: 2. Prove that, V{(sec 0 - 1)/(sec 0 + 1)} cot 0. = cosec e

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Q: What is the trigonometric form of equation z = 40 e i 120º O z = 40(sin 120 +j cos 120) O z = 34.64…

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Q: A particle moves in simple harmonic motion according to the equation, s=25Acos(wt)+25|B cos(wt).…

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Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

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Q: 3 and t <Os, then sece is equal to: 5 37t - 1. If sin 0 - 5 a) 4 4 b) 5 4 c) -

A: Given:  sin θ = -3/5     π ≤ θ ≤ 3π/2

Q: 2. sin 8 = 42 P(0) is in the second quadrant

A: Given θ lies in the second quadrant We know that sinθ , cosecθ are positive in the second quadrant…

Q: What is the exact value of cos 165° V2-V6 4 V2+v6 4 O V6-V2

A: Solution of the problem as follows