TAKE THE ABSOLUTE VALUE OF YOUR ANSWER! torven: - 2T -T 271 a ftt)= Cos nt Fourier Series si か。 find; a+b+c

Q: Represent 701lowing fundtion The fourier Sine Serie's किप AISO draw graph.

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Q: 3 Prove the identity: sin30 = sin® –sin30 using De Moivre's theorem.

A: To prove the given identity ,we have to use De Moivre's identity.

Q: (1- cos 0)(1+ cos 0) = sin´ e

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Q: p2 cos 20 = 1 COs

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Q: ー1 B Cos (2 oin (oen 3 + cas の An

A: Sin(A+B)=sinAcosB+sinBcosA

Q: -1 cos х ах

A: We can find the answer to the integration in the following steps.

Q: Determine the volume of the solid that is below the 3x+2y+z=12 plane and above the retangulo R={(x,…

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Q: Find the product of z1 & Z2, leave answer in trigonometric form: 235 (cos플 + isin) & z2 =: +i sin 3…

A: We know that for  z1 = r1 cos θ1 + i sin θ1  and  z2 = r2 cos θ2 + i sin θ2 z1·z2 = r1·r2 cosθ1+θ2 +…

Q: tan² 0 – sec² e :

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

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Q: Evaluate e sn® 3x cos*3x dx 9 512 O 157 512 О Зя 512 512

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Q: Use the factor formula to prove that sin 5° + cos 35° = sin 65°.

A: Explanation of the answer is as follows

Q: Express each one of the following in the standard form a + ib. 1 A: (1 + i)? (iii) 3 - i 3+4i 1+i…

A: standard form , a+ i b first part = a (real part second part = i b (imaginary part

Q: Derive the cosine formula a2 = b2 + c2 – 2bc cos A and the sine formula sin A sin B sin C а b C…

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Q: Express the following in Cartesian form

A: As,  cos 300o= 12 and sin 300o= -32. Now, put the values and simplify.

Q: Prove that v2 cos(20+45°) = cos e-2sin Ocos 0-sin 0, where 0 is measured in degrees.

A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB. sin2A = 2sinA*cosA. cos2A = cos^2(A) - sin^2(A).

Q: Use De Moivre’s theorem to write (cos π/5 + i sin π/5)^5 in the form of a +bi

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Q: Using csc 8 = ±√1 + cot²0, express csce in terms of cose only.

A: We are asked to express cosec interms cos

Q: Express as a sum.(cos au)(cos bu)

A: Given : (cos au)(cos bu)

Q: 1. Answer the following questions based on the graph below: a f d e a) Find the number of verticals…

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Q: (1) I= 3 Cos 2x do dx 1+51n2

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Q: 2 n ) Compute sin . An exact answer is required. 3

A: Answer and explanation is given below

Q: Prove the half-angle identity sin A/2 = ±√((1 - cos A)/2)

A: Consider the identity

Q: etermine the fifth roots of 32 cos 5 T 6 + i sin 5T 6

A: Solution :-

Q: Exercise 2. (a) Let z = a + bi, and express a cos(wt) + b sin(wt) in terms of z, z, elt, and e-it.…

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Q: Using Euler's formula ete = cose + i sine %3D Show that el0 +e-10 et0-e-10 cose = sino zi

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Q: COS 10T - i sin 10TT 3 3 GT+ 3 of 學 4T COS 27 + 40 3 C1) - 1 2

A: Use trigonometric ratios

Q: Find cos theta is sin theta = 1/2 and theta terminates in QII

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Q: 3. Express M =cos 3A+cos A and N = sin 3A+sin A as a product form. M = cot 2A. N Hence, show that

A: topic- trigonometry

Q: Calculate d66 (sin 0) d066

A: Let's see some derivate formulae 1. ddx(sinx) = cosx 2.ddx(cosx) = -sinx

Q: Compute the exact value of 13 T sin 12

A: Given query is to find the exact value of given sin function.