1:56 ) A A O 为 O * X i al60% 4 of 5 Complete the steps by applying trig identitles to show that the left hand side of the equation Is equivalent to the right hand side. sec a - tan z· sin a sec Steps: Sec a tan z sin a sec z sin : 1+ 1-coa ain Nin - coS : 1+ tan. :1+ · sin" a sin a sin a sin r cus a CUS cosain" sin sin 1-sin' -sin' cas' Cos sin + sin" z. sin ! cos sin z sin' CUB San 2 : cos z sin r Next :: ::

Q: 3. Given the function y = 4 cos(2x) + 6, where y is measured in metres and x is measured in minutes:…

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Q: 0 and 02 are two distinct values of 0(0 < 0127,0< 02 < 2x] satisfying the 1 sin 2a. Prove that, 21…

A: Consider the following equation: sinθ+α=12sin2α Substitute θ=θ1 and θ=θ2 in the above equation:…

Q: Which of the following completes the missing step to the following proof. cos? 0 1- sin 0 = 1+sin 0…

A: We use Trigonometry identities

Q: (1–tan? x) = cos x on the domain 0 < x < 2T. Solve (1+tan? z) 27 O T, 3 п, 품, 뚱, 47 3 27 O , , 2ㅠ 57…

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Q: Given f(0) = 7 cos 0 + sin 0. %3D a. Express f(0) in the form of R cos (0 – a) for R > 0 and 0° < a…

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Q: 41. A 16-foot-long trough for feeding cattle is shown above. If x = 1.5 feet, which of the fóllowing…

A: Step:-1 Given that  a 16 ft long trough and x= 1.5 feet Note:- In this figure, if we take ABC as…

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Q: Find the length of the path for c(t) = (4(0 – sin(0)), 4(1 – cos(8))) over the interval 0 < 0 < 2r.…

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Q: Eliminate the parameter t in the following. x = 6 + 4 tan t, y = 4 + 4 sec t

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Q: The rose - Firnt patal is given by the equation Select one: OT= 5 sin 80 where 0 E [0, 27]. OT=5 cos…

A: Given:          From the above graph the rose has 8 petals.    The polar equation r = b.coskθ , 0 ≤…

Q: 1. Let z = 3+ 6i find exp(z) in x + iy form. 2. Let exp(2) = 2 + i find z in x + iy form. 3. Find…

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

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: 1. (a) Use integration by parts to verify the reduction formula cos" x sin x n Scos" xdr = -1 [cos"…

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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: 2. Let r and y be real numbers be such x, y E {6i 3 2 2 3弧,T} T T T T (a) If 4 cos (2t) dt = find x.…

A: Here integral is already solved and answer is given in term of f(x) and g(y). Which is true because…

Q: Let z(x, y) = xy where x = r cos(80) & y = r sin( - 50). %3D | дх ду дх ду & ar' ar' a0 az dz & ar…

A: Let z = f(x,y), then,   ∂z∂r =∂z∂x · ∂x∂r + ∂z∂y · ∂y∂r   ∂z∂θ =∂z∂x · ∂x∂θ + ∂z∂y · ∂y∂θ

Q: The following integral 9- dz around the circle z-7| 1 yields: sin z -i2n i2n zero None of these نقطة…

A: Use Cauchy Integral Formula to find out integration.

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 the speed over the path r(t) = (sin(3t), cos(6t), cos(3t)) at t = (Use symbolic notation and…

A: The path r(t)=sin(3t),cos(6t),cos(3t) at t=π2

Q: An RL circuit has an emf given (in volts) by 3 sin 2t, a resistance of 10 ohms, an inductance of 0.5…

A: Given,             dIdt+20I=6sin2t                        ...(1)and  emf=3sin2t…

Q: 5. Find the principal value. (*). b) tan (aresin 4) a) cos (4) 6. Solve for all solutions where 0 <r…

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Q: 13.2. Find the length of the arch of the cycloid given by z(t) = a(t – sin t) + a i(1 – cos t), 0 <t…

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Q: A ladder of length AB is carried horizontally through an L-shaped turn in a hallway. A Show that the…

A: Given,

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A: Graph of a(x) is  Graph of b(x) is

Q: a) Find all exact solutions on [0,2n) of 8sin?x + 6sinx + 1 = 0. b) Fine all exact solutions on [0,…

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Q: (a) Find an approximate value for the integral cos? r dr using the Composite Simpson's rule with N =…

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Q: Express the number 3√3 - 5i in the form R(cos(0) + i sin(0)) where R> 0 and -T≤0 ≤ T. NOTE: Round…

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Q: (a) Consider the ODE y' + tan(ax)y = sin(ax), where a is a nonzero real number. Find an integrating…

A: “Since you have asked multiple questions, we will solve the first question that has been asked. If…

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

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Q: Find all values of 0 in [0; 2n] that satisfy the equation. 3. 2 tan(0) - sec(0)sin?(0)=0 3TT 7T a.…

A: Given: 22tanθ-secθsin2θ=0, θ∈0, 2π

Q: Assume that x, y ER and z = x + iy E C and answer the followings: 1. Evaluate sin(i) =?, cos(i) =? ,…

A: Since the questions contains many subparts as per the guidelines I am answering the first three…

Q: 1. (a) Use integration by parts to verify the reduction formula l(cos"-² x dx cos"- xsin x, n–1…

A: Solution:Verify the reduction formula∫cosnx dx=cosn-1x sin xn+n-1n∫cosn-2 x dxDerive the Wallis…

Q: A. 5 cos 0+3sin? 0 = 3+2cos 0 B. cos x(secx - cost) = sin? x %3D 1-2sin? 0 С. sin ecose = cot 0-…

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Q: 0.2 Use Euler's identity to (a) show that (i) cos(0 – 1/2) = sin(0), (ii) – sin(0 – 1/2) = cos(0),…

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Q: Eliminate the parameter t in the following. x = 4 + 3 tan t, y = 6 + 3 sec t

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Q: 1/2 cos t Evaluate the integral o dt. 4.- sin? t In a Give your answer in the form where a and b are…

A: Given: ∫0π2cost4-sin2tdt Let sint=xcost=dx Then sin0=0sinπ2=1 So, ∫0π2cost4-sin2tdt=∫01dx4-x2

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: (d) Show that 1– ei(n+1)0 1 – eie ei(2n+1)e/2 ,-i0/2 - e 2i sin(0/2) Hint: Factor e!6/2 out of the…

A: 1-ein+1θ1-eiθ=1-ein+1θ1-eiθ÷eiθ/2eiθ/2                       =e-iθ/2-ein+1-12θe-iθ/2-eiθ/2…

Q: 1) Find the fundamental period of the functionu +v, if any, by examining whether the functions u (t)…

A: All trigonometric functions are periodic. To find if ut=sin2t is periodic: Express it in terms of…

Q: 8. Which numbers in the set ,T, 2n are solutions to the following equations? a. sin x C. 3 secx = -…

A: As per our norms we have to write three multiple questions at a time kindly repost remaining…

Q: b. Determine real (e/z) in terms of x and y. C. Use Euler's formula to prove that expression; = cos…

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Q: Given that 7(1 + h) – 7(1) = (h - 1 + cos(h), e" -e-", In(2h + 1)) for all h where -. a 7'(1 :…

A: We will use the definition of derivative to find r'(1) as shown below

Q: 40 0<0<-, find the exact valı 41' If sin 0 = (a) sin (20) (b) cos (20) (c) sin 2 -

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Q: 1. (a) Use integration by parts to verify the reduction formula Scos" xdx = cos"- xsin x n-1 +-…

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.