- 1T then 4 - If 0 = %3D sin(0) = %3D cos(e) COS Give exact values. No decimals allowed!

Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

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Q: Suppose that 1 a + sin x ) dx = 15x 1 + x2 -1 What is the value of a Your answer should be an…

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Q: 1. Find the value of A between 270° and 360° if 2sin²A – sin A = 1 |

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Q: 4-If y= cos 8t , find the frequency (w) and the fundamental period(T.) 5-If: y = (sinx+1) (cosx+1)'…

A: We know that, The fundamental period(T0) of cos(x) = 2.pi                            if cos(ax) = (…

Q: Solve for the value(s) of x over the interval 0 < x < 360 2 cos x + 1 = 0 %3D

A: We have to find values of x over the interval 0&lt;= x &lt;= 360 of the equation 2 cos (x) +1 =0.

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&gt; 0

Q: 3. у %3D In(5 — е**) 4. x = et (cos 2t + 2 sin 2t)

A: Now the first given function is ln5-e4x The second given function is x=etcos2t+2sin2t To find the…

Q: sin x – e-* = 0, [0,1]

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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: S (1) Find the general solution of the equation IC sin x+ 6. 2 cos x %3D

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Q: Find all solutions to 2 cos(0) V2 on the interval 0 < 0 < 2A = |

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Q: 3. S cos ædæ from a = 0 to b = 5

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Q: If k0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to [−sin(kx) + sin³(kx)] + C the…

A: To evaluate the integral.

Q: cos 3t dt 5 + 3 sin 3t Ocos 3t

A: Given- ∫cos3t dt5+3 sin3t We have to find u which is used in evaluating the given integral and to…

Q: Find values for b and c that will make ƒ(x) = sin (x + a) and g(x) = b sin x + c cos x satisfy the…

A: Given functions are fx=sinx+a and gx=bsinx+c cosx. We have to find values of b and c for given…

Q: 1.)When m is odd, we can integrate sin" (x) dæ by letting u cos(a). Why does have to be odd for this…

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Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

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Q: 1. Eliminate the arbitrary constants on the given equation: -= C, cos 3r + C2 sin 3x

A: Elimination of the arbitration constants

Q: Solve the following equation on the interval 0se<2T. sin 20+ + cos 0 = 1- sin e

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Q: 3- If a y + sin y + arctan a = sin 1 then what is the value of at (0,1)? dz -2 b)- 1+ cos 1 -1 1 a)…

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Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: 9 Find 0 if 0<0 < 2n and: d sin 0 = 1 h cos? 0 = i tan 0: i tan? 0 = 3

A: To find θ if 0 ≤ θ ≤ 2π  sin θ = 1cos2 θ = 12tan θ = -13tan2 θ = 3

Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx-

A: To evaluate we first multiply and divide by 2 the given function.  Then use the formula: 2(sin(mx)…

Q: If sin x = siny = a and cosx = cosy = b, then cos(x-y) is Select one: O a. z2 + a² O b. 2b + 2a O C.…

A: Given  sin x = sin y = acos x = cos y = b Use cos (x-y) formula cos(x-y)=cosx cos y + sinx sinysin…

Q: 2ä + 2i + x =1 with x(0) = 0 and ¿(0) = 2 Answer: x(t) = 1+ 3e-0.5t sin 0.5t – e-0.5t cos 0.5t

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Q: Find: L [sin 2 5t ]. 0-co 5 Cos 10t) s² + 25 O A.) B.) 1 5 s² +25 2s 2(s +100) C.) D.)

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Q: IFS(x) = - sin(x), then S ® (1) is equal to - sin(x) B) - cos(x) sin(x) O cos(x)

A: We have to solve

Q: Solve the equation for 0 if 0° <o<360°. cos 0 + V3 sin 0 = -/3

A: 1. cos θ+3 sin θ=-3 Note:    Multiple questions are given, we are answer with only one question. If…

Q: = -1, find the value of can 0-1 sin 0 – 3cos e sin 0 + cos 0

A: Given thattanθtanθ-1=-1Sotanθ=-1(tanθ-1)tanθ=-tanθ+12tanθ=1tanθ=12

Q: the solution to the given equa y" + y' – 2y = cos(x) – 3 sin(: -

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

Q: i) L-- (In) L- | s-3 6s+3 ii) L-1 iii) L(tet cos wt) s+1 sª+5s2+4,

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Q: 2/12 6. If sin(t) =- and cos(t) < 0, find the exact value of tan(t). %3D

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Q: 1. Given x = r2 cos(20) and y = -r² sin(20)

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Q: 2 10) Given sin A = - where <B<n , find tan(A+B). 2 < A< T and cosB where 4

A: Please refer to the image

Q: 47. Show that y = sin(tan-x+ C) is the general solution of y' = /1 – y²/(1+x²). Then use the…

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Q: 9. 3 cos(wt –@), where w and a are constants.

A: We use first Cos(a-b)=cos(a) cos(b)+sin(a)sin(b) and then we use Laplace transform of…

Q: e. Find sin (x – y) given that sin x = 8/17 with 0 < x < 90° and cos y = -24/25 with 180° < y< 270°.…

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Q: _5. In the equation y = sin-1 x, if = , then y= TC %3D %3D %3D

A: 5. In the equation y=sin-1x , if x=12 , then y=π6. The given statement is True, The reason regarding…

Q: 4. Prove that the identity is true. 1- cost e = sin² 0 1+ cos e

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Q: Find all solutions to cos(7t) – cos(3t) = sin(5t) on 0 <t <n 1

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Q: 1. S" cos? (2t) dt u-sub = 2. S sin5 0 cos* 0 d0 power on sin is 'odd'

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Q: Find cos (0 + p) given that cos 0 = 2 and cos p = 2 and that 0 and p are between 0 and t/2.

A: For the given values of  Cos(θ)=1213 Cos (ϕ) = 35 Cos(θ+ϕ ) is evaluated as shown below

Q: 4. Given 0<0 < 2T, solve 2 tan 0+sin 0 cos 0 = 0. O 0, T

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Q: 1. Given sinx 12 and cos y : 13 both x and y lie in sxs, determine a) cos(x+y) b) sin 2y

A: Given query is to find cos(x+y) and sin2y.

Q: sốn ² sin () cos() sin() dx (Consider initially the first 2 terms)

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Q: Solve the following equation on th e interval [0, 27]. cos x + 2 cos x+ 1 = 0

A: Given : cos2x+2cosx+1 = 0

Q: 10. If y = sin 2x + cos 2x, then (yn)o is equal to nn a) (-1)"2" b) 2" c) sin+ cos d) None of these

A: The solution is given as

Q: "+25y 4r sin(51) – 2e" cos(5t)

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Q: 3) Find the exact value of cos(a + B) under the given conditions. V5 0< a < sin ß = - -< B < 0 4 TC…

A: We know thatcosα+β=cosα cosβ-sinα sinβ

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.