given cosθ =3/5, 3π/2 ≤ θ ≤ 2π and sinβ= -12/13; π ≤ β ≤ 3π/2; determine the exact values of the following:  a) tan2θ b) sin(θ+β)

Q: If a, B, y, ð are the smallest positive angles in ascending order of magnitude which have their…

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Q: , Find the exact value of cos (a – B) given that cos a = - and sin 3 = -0 for a in Quadrant III and…

A: We have to find the value of a trigonometric expression involving two angles.

Q: Given that 4 cos z - 2 sin z= a cos 2x + b, the values of a = %3D and ||

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Q: Use the exact values from show thatthe following are true.   cos 2 theta 30 0   + sin 2 30 0 =1 cos…

A: The values you will use : cos30∘=32sin30∘=12cos45∘=12sin45∘=12

Q: Which of the following is equivalent to sin 0 csc 0 sec 0 for all values of 0 for which sin 0 csc 0…

A: To find the equivalent form of the given expression apply the following formulas.

Q: 1. (a) Use the Wallis cosine formula to evaluate [ cos' x dx.

A: We need to find  ∫0π2cos9xdx by using Wallis cosine formula. We know that,  Wallis formula ,  If  n…

Q: Given the sin(a) = -8/15 and tan2B = 12/5, where a and 2B lie in the interval (3t, 71/2), compute…

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Q: . Find, without using tables, the values of Cos x and Sin x, when Cos 2x is : 1/8

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Q: Given that sin' (x) and cos (x), show that sin(a+B) = 1 %3D

A: Use the identities of inverse trigonometric function.

Q: If it is known that sin a = and < a <n and cos ß = -- and <B < , find the exact %3D value of cos(a +…

A: cos2 α+sin2 α=1  Substitute sin α=13 in the above trigonometric identity: cos2 α+132=1 cos2…

Q: 6) Let sin 0 - for n <0 < Find the exact value of: %3D 2. a) cos 0 b) tan 0

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Q: A right-angled triangle xYZ has an angle, o, where sin o = 5. Without evaluating &, calculate the…

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Q: 4. The definition of cos e using right triangles applies when (choose the correct answer): (b) 0 < 0…

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Q: If 0 = then 3 %3D sin(8) = %3D cos(e) = %3D

A: We have  this can be also written as

Q: The imaginary part of G(jo) is equal to zero if find: w Hence, sin 0.80 + w cos 0.8@ = 0

A: Complex number Z=X+iY X=real part of complex number  Y=imaginary part of complex number

Q: 0≤θ<2π, , solve 2tanθ+sinθcosθ=0.

A: 2tanθ +sinθ.cosθ =0, θ : 0⩽ θ &lt; 2π ⇒let alternate forms, ∴2tanθ + sinθ.cosθ=0∴2sinθcosθ+…

Q: It is given that sin a + sin b = /5/3 and cos a + cos b = 1. Determine the exact value of cos (a -…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Let sin A 13 12 with A in QII and sin B 3 with B in QIII. Find sin(A + B), %3D - 5 cos(A + B), and…

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Q: Find the values of the remaining circular functions of 8, with the given conditions. 1. tan 6 = sin…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: If cos A = with A in QIV, find the following. 2. sec A

A: To find the value of the following half angle,

Q: Find the exact value of cos a/2 given that tan a = 15/8 ,a lies in Quad III.

A: Given: tan a=158 a is lies in Quadrant III. We have to find the exact value of cosa2 Use the…

Q: Find the length of the path over the given interval. (5(θ − sin θ ), 5(1 − cos θ )), 0 ≤ θ ≤ 2π

A: Given function is  rθ=5θ-sinθ,5(1-cosθ) 0≤θ≤2π

Q: Given ∆JKL, sin K= , cos K = , tan K = \

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Q: Find the exact value of the following under the given conditions:a. cos(α + β)   b. sin(α + β)   c.…

A: given: tanα=-34, α lies in quadrant II cosβ=13, β lies in quadrant I we have to find the exact…

Q: 10. What is tan 315° + cos (-570°) equal to? V3 b. a.- (1+4) а.-1 V3 d. 1 -

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Q: If sin a and cos a3D 13 12 what is the value of sec. 13 %3D O 13/2 O 13/2 17 O 17/2 26 O 7/2 26

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Q: Find the exact value of cos(A+B) if sin A = with A in QI and sin B 5 with B in QID = -

A: Given: sinA=35sinB=-513 To find the exact value of cos(A+B) COS(A+B)=COSACOSB-SINASINB COS2θ+SIN2θ=1

Q: The value of So" 6 (4+ cos2x)dx is:

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Q: Given that cos 2a = - and 180° < a < 270°, find tan a O 2 1 V5 O -2

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Q: 3. Given that cos 30 J3 and sin 4S = 2, without the use of a %3D %3D 2. 2. calculator, evaluate…

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Q: Given that cos x = 4/5 and x lies in QIV, determine the exact value of sin x/2

A: Use the formula cos 2θ=1-2sin2θ and substitute x2 for θ and then 45 for cos x.

Q: Which of the following is equivalent to cos (60° + 0 + sin(30° + 0)? cos 8 +V3 stn 0 cos e Option 1…

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Q: Given that sin(x) = 11/61, and 0<x <<x< pi/2 %3D Find cos(2x).

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Q: with A in QIV, find the following. If cos A = sin A 스2

A: We have given cos A = ½ with A in QIV.

Q: Compute the exact value of 13 T sin 12

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

Q: Let cos(16°) 0.9613 What is the the value of r, in degrees, for sin(z) 2 0.9613 ? Submit Question

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Q: Given tan A = -% and cos A < 0, determine sin A. O 4/5 O 3/5 O -3/5 O -4/5

A: Let's find.

Q: If sin A = 3/ 4with A in QII, find cos A.

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Q: 1. (a) Use the Wallis cosine formula to evaluate [ cos° xdx.

A: Given, ∫0π2cos9xdx

Q: 1 Assume that cos(0) and 0 is in the first quadrant. Compute the following using the double 5 angle…

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Q: Determine the exact value of cos(330)° V3 2

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Q: By sum or difference identity, the exact value of cos 105° is: 2 + 6 V2 - V6 4 + 4 4 V3+ V6 4 2.

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Q: Use the given information tan α = 4/3, 180° &lt; α &lt; 270° to find the exact value of the…

A: To Determine: use the given information to find the exact value of the following  a)  sinα2   b)…

Q: Determine the guadrant in which the terminal side of 0 lies (a) cos 0 0 (Choose one) (b) sin 0 < 0…

A: Given that  A) cosθ&lt;0 and sinθ&gt;0 b) sinθ&lt;0 and tanθ&lt;0

Q: By an appropriate trigonometric substitution, Choices: √ √10 sin sin 0 cos de cos √10 sin 0 1 /10…

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Q: Determine the value of sin a + cos a for a = 20 degrees. %3D

A: Here we have to evaluate the value at given x.

Q: uppose θ is in the interval ( π/2 , π) and sin(θ) = 1/5 . Evaluate the given quantities exactly, and…

A: sin θ = 15cos2 θ = 1 - sin2θcos2θ = 1 -(15)2 cos2θ = 1 -125cos2θ =2425cos θ = 265