Q2/ Evaluate the following: 1- Prove sin 2x+cos2x+1 sin 2x-cos 2x+1 cot x 2- Sinh (u-v) = Sinh u.Cosh v- Cosh u.Sinh v 3- If tane=3/2, find the value of sece and sine without using table.

Q: 1. Use the trapezium rule to estimate the value of the following correct to four decimal places a) |…

A: 1a) It is required to estimate the value of ∫0π3tanxdx with 4 strip using trapezium rule.

Q: 5. (a) Expand (1+x) and hence find the value of (1.02) correct to 4 decimal place 1+sin 0 m-1 1-sin…

A: First expand 1+x4 then find the value of 1.044 Using the identity, a+b4=a4+4a3b+6a2b2+4ab3+b4…

Q: Write the function f (a) = – sin(3a) – v3 cos(3a) using a V CoS - single sine function and use the…

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Q: 4- Using the data sin(0.1) = 0.09983 and sin (0.2) = 0.19867, find an approximate value of sin…

A:

Q: Find F(1). sin (2t) + cos (2t). use 2 decimal places. Answer: 0.33

A: Given- 12sin2t + 23cos2t To find- Find F1. Use 2 decimal places.       Formula Used-  ℒsinat = as2…

Q: Use Newton's method to find solutions accurate to within 10-5 for the following problems. a. ex +2-X…

A: Consider the given equation and interval. ex+2-x+2cosx=0 for 1≤x≤2   The formula for Newton's method…

Q: 2 Given tan 0 = -and sin 0 > 0, find cos 0. %3D Cos 0 _ 3/13 13 О А. O B. cos O 0 = 3/13 COS %3D 13…

A: The given data is: tan θ= -23  and  sin θ> 0

Q: Solve the following: √ ( sin 3x e3x 0 + 2) dx + 2x³ sin 2x) dx 2. 3. f sec x (secx + tanx) dx 7.…

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Q: 1. Determine solutions to sin 2x = , xE [0,2x] 2x sin () accurate to 2 decimal places. 2x 0.73 X0.36…

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Q: Note: Answers must be in 4 decimal places. 1.Use De Moivre's Theorem to solve the following. I. Find…

A: We are entitled to solve one one ques at a time and up to 3 sub-parts only. To find - Use De…

Q: 3 T 3. Find the exact value of sin 8. 1 + cos 0 - cos e 1 = + cos = ± sin cos O tan 1 + cos 0

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Q: 3TT Find sin (sin 0), if n<0< 2 -1 Select one: O e+ t O e-T

A: To find: sin-1(sinθ),   if π&lt;θ&lt;3π2

Q: 06:- Find the result of the following. (Choose two only) 4 1- 2-Si(Vx+ dt OLLI x² 3- 7 sine do

A:

Q: The displacement x of a moving object at time t is given by the equation x= sin (2t)cos (2t) For…

A: Given integral is ∫sin42tcos32tdt

Q: Q1. Find one of the roots smaller than 5 of the following equation given below by using graph of the…

A: We draw graph of given function when a=7. And then find the roots below 5 by observing the graph.…

Q: Please find all 0 <0 < 2n, for which .. (a) tan () = v3 (b) 3 sin? (0) + 4 = 5 (c) 2 cos(ln(x² + e*)…

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Q: f(A) is an odd function, and deduce that for each x E R the value of the c) Show that integral 3A…

A: From part (a), the function f⏞λ is defined by f⏞λ=i2π3λcos3λ-1λ2sin3λ Relacing λ by -λ,…

Q: Calculus 11th Edition - Ron Larson Please assist with the question below. Please show &amp;…

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Q: If the equation of motion of a particle is given by s = A cos(@t + 8), the particle is said to…

A:

Q: Given the integral sec (x - 1) tan4 (x-1)dx, which of the following equations will be useful for…

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Q: Calculate for one real root of tan a = 4æ with ao = 1.2 up to four decimal places using the…

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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: Let ( f(x)=cos(x)+2xe^x ) Use the secant method for finding the biggest negative root. Conduct two…

A:

Q: 3) Solve the following equations over the given interval. a) 2 sin(8) - 4 =-2 sin(0) over [0,27) b)…

A:

Q: S By an appropriate trigonometric substitution, S: I 1 √10 sin 0 cos² Ode Cos 0 10 sin 0 -do |…

A: Here we will use Trignometric sunstitution for given integral.

Q: Q5. a) Suppose tan x = - and x is in the second quadrant. Then find: (i) sec x (ii) cos x (iii) sin…

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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: exp (еҳp(-in)) cos TT - i sin T 0.3679 - exp(cos t - i sin Tt) -0.3679

A: solution of the given problem is below...

Q: When two water waves meet on a pond, they combine such that when 2 crests meet, they are added to…

A: Graph of a(x) is  Graph of b(x) is

Q: Assume sin(0) = = 19 29 sin (0+) = sin(0 - 0) = cos(0 + 0) = cos (0 - 0) = where << π, and cos(p) =…

A: Given

Q: Two masses hanging side by side from springs have positions s1 = 2 sin t and s2 = sin 2t,…

A: (a) Obtain the time in the interval at which the masses pass each other as follows.

Q: 3. (a) Use an appropriate factor formula to express sin(x) + sin(3x) as the product of a factor of…

A: (3)According to question factor formula to express (sin x+sin3x)As we know that sin(A)+sin(B)=2…

Q: - Using Lagrange interpolation formula, find the value of sin points 6 X: 0 π/4 π/2 sinx: 0 0.707107…

A:

Q: i. Find the domain and range of f(x)=2 cos'(4x– 3)–“ and sketch the graph 4 ii. Find the general…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1 Evaluate Le' cos 2t +÷sinh 2t

A:

Q: What is x1 if Newton-Raphson is used in the function f(x)=5sin^2(x) -8cos^5(x) with the initial…

A: fx=5sin2x-8cos5x , x0=0.5 Differentiating f wrt x, we get…

Q: (e) Solve for x 4 + sinh(3x) = 4 cosh(3x). (f) Using Euler's formula, ei = cos 0 +j sin 0, derive…

A: This is a question from hyperbolic functions and complex analysis.

Q: 1. Determine solutions to sin 2x , xE [0, 2x) 2x = sin () 2x 0.73 %3D accurate to 2 decimal places.…

A:

Q: Given the following integral of a trigonometric function raised to an odd power dx and its…

A: Given that  The integral is  To find the value of integral by using the trigonometric substitution

Q: Using the Taylor's formula calculate cos 9° n=5.

A:

Q: 6. In right ALMN with right angle at N, sin L 4x-0.22 and the cos M 2x+ 0.28. Determine and state…

A: Given; sin=4x-0.22 and the cosM =2x+0.28.

Q: The displacement x of a moving object at time t is given by the equation x= sin (2t)cos (2t) For…

A: Topic = Integration

Q: 3. (a) Use the substitution x = 2 tan 0(-1/2 <0 < T/2) in the expression T/V4+x2 and show the result…

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Q: 5. Evaluate SO-2²πT ydx = 3π₁ given x = 0 - sine, y = 1- cos -0

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Q: 12 and x terminates in guadrant I. 13 Find sin 2x, cos 2x, and tan 2x if sinx= sin 2x %D cos 2x %3D…

A: Given: sin x=1213and x terminates in quadrant I. To find sin2x, cos2x, tan2x The hypotenuse side is…

Q: I. Determine the exact values of each of the indicated trig functions for the problems below 8. sin…

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Q: 9. Find all values of x in the interval [0,360°) that satisfy each equation. Round approximate…

A: a) 2sinx=cosxsinxcosx=12tanx=12x=tan-112x=26.6°, 180°+26.6°x=26.6°, 206.6°

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.