If P = A sin 0 + B cos 0 and Q = A cos 0- B sin 0, find the value of A2 + B² in terms of P and Q. А. Р- Q В. Р+Q C. p2 - Q D. P2 +Q

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

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Q: between 0° and 360°. z, = cos 100° + i sin 100° Z2 = cos 230° + i sin 230° %3D Choose the correct…

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Q: Which of the following is equivalent to | cos(4a)sin (4x) da ? cos udu · 1 sin udu, where u = 4x…

A: The answer is found in step-2.

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

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Q: uppose that sin x= -1/2 and pi < x < 3pi/2 and that tan y= 5 and 0 < y < pi/2. find the following…

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Q: If sin (B) = -1/5 with B in QIII, find cos (B/2). cos (B/2) =

A: We have to determine the value of cosB2 when sinB=-15 We know that…

Q: If x = 4 sin 0, then J csc2ede = %3D

A: Here, ⇒x=4sinθ⇒sinθ=x4 By using Pythagoras theorem, We will have remaining side of the triangle…

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 cos A with A in QIV , find sec %3D a. sec | b. sec 2. с. sec A d. sec 4-5 %3D A sec e. A2 1/2 II…

A: Since you are asking multiple questions. We are answering only the first question. Given, cosA=18…

Q: Find a solution for sin (O + 15°) = cos (20 + 30°). %3D

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Q: If z = 1+ 2i and w 3+ 4i, express in rectangular form 5 cos [Arg (2²)] + 5i sin[Arg w]

A: The square of a complex number z is the product of z with itself. Multiply 1+2i by 1+2i to obtain…

Q: From the formula of sin (A + B), deduce the formulae of cos(A+ B) and cos (A- B).

A: To derive formula cos(A+B) &amp; cos(A-B) using formula of sin(A+B)

Q: Which set of values is the is the solution for (2 sin x +1)(cos x - 1) - 0 ,0 sis 2n ? 7. 11 1 5 7…

A: Given that, the equation is 2sinx+1cosx-1=0,x∈ 0,2π. Rewrite the 2sinx+1cosx-1=0 as,…

Q: Given sin 0 = , where < 60 < , determine the value of cos VTO 10 3/10 10 O 3V10 10 10

A: We use cos (x)=√(1-sin2x) and cos (x/2)=√((1+cosx)/2). Thus ,option c is correct answer.

Q: If cos A =and sin B= =, where P (A) and P (B) are both in QI, find sec(B – A). %3D O 4/6+v21 3.…

A: topic - trigonometric identities p

Q: Assume that sin A = 0.81, cos A = 0.59, sin B = 0.91, and cos B = 0.41. Find the given quantity…

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Q: If w=f(a,b,c)=cos(ab)sin(b)+c, what is at ( -,6

A: Given function and point is  w=f(a,b,c)=cos(ab)sin(b)+c and 12,π3,6

Q: In AXYZ, the measure of ZZ=90°, the measure of ZX-20°, and XY = 73 feet. Find the length of ZX to…

A: Use the trigonometric ratio as it is right triangle.

Q: 22. Given that4 cos 0 + 3 sin 0 = R sin(0 + a), the value of R and tan a are respectively 3 A 25…

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Q: 3. Find cos a if sin a

A: Given:sinx=910cosx=?Formula:cos2x=1-sin2x

Q: If u(t) = (sin(7t), cos(7t), t) and v(t) = (t, cos(7t), sin(7t)), use Formula 5 of this theorem to…

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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: . If 180° <0 < 270° and cos 0 = -, find cos . 15 O 2v15 15 O - VI5 15 O V15 15 O - 2V15 15

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Q: please answer all the parts

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Q: Solve the equation for æ if 0 < z < 27. Separate your answers with commas. 2 cos(2x) – 6 sin z = 4…

A: Simplification

Q: If sin A 315 3π 2 where π < A< then cos 2A =

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Q: For what angles O between 0° and 360° is v3 cos 0 = Sin ĕ true?

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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: If cos a = 0.565 and cos ß= 0.867 (both angles are acute),

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Q: 19. Writc the ratios for sin B and cos B. a. sinB cosB 5 b. sinB cosB 5 %3D C. sinB cosB = %3D d.…

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

Q: If sin ZC AB= and AC = 15, what is the value of cos ZC AB? %3D O 1

A: Given Data: The length of the side  AC is: AC=15 The sine of the angle CAB is: sin∠CAB=35 The sine…

Q: Find (a) sin(?) and cos(?), (b) tan(?) and cot(?), and (c) sec(?) and csc(?). Assume x = 7, y = 9.…

A: First we shall solve the given trianlge. Now we shall find the third side using pythagorus theorem.…

Q: Find zw and Leave your ans z=3(cos 140° + i sin 140°) w=5(cos 280° + i sin 280°)

A: Given that,

Q: b. Given that z = el®, show that z" += 2 cos ne. Hence, show that cos 50 = 16 sint 0 – 112 sin² 0 +…

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Q: 15. Use the formula cos(2x) = 1 – 2 sin? z to find cos , if sin O V? O va 2

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Q: If cos (0) = - and sin (8) = -, where <0 <r and <B< 27, find cos (0 + B). 5 %3D %3D 13

A: Given,            cosθ=-35 and sinβ=-513 , where π2≤θ≤π and 3π2≤β≤2π

Q: Find (a) sin 2t, (b) cos 2t and tan 2t given the following: 1) cost = −5/13 , and π/2 0 3) tant =…

A: The detailed solution is given below Thank you

Q: 2. If sin A = -35 with A in QIII and cos B = 5 13 with B in QIV, find the following. a. sin (A + B)…

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Q: Use the formulas 1 1 i0 cos 0 = (e" + e-) and sin0 = 2i to obtain the identity 1 (cos 40 – 4 cos 20…

A: See the detailed solution below.

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 -10 cos wt + 4 sin wt = A cos (wt + ), where A>0 and -180°<$ < 180°, find three values of t, 0 <t…

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Q: D. If 180° <0 < 270° and cos 0=-, find cos 15

A: We have been given the range for the angle from 180 degrees to 270 degrees.

Q: for which a applies that tan(a) = 2 and that o<a< I. Decide a) sin (a) B) cos(a)

A: Please see the below picture for detailed solution.

Q: 2. Use Euler's formula to prove the following expressions: (a) 1- cos(20) sin? ø 2 (b) sin(20) = 2…

A: The objective is to prove the following expressions using Euler's formula 1. sin2ϕ=1-cos2ϕ2 2.…

Q: ди du and ar if u = e" cos 0 . cos(r sin 0) (1) Find

A: It is partial derivative

Q: Given P(A) = (4, -3), what is the value of of cos %3D A?

A: Given that P(A)= (4,-3), Our Aim is to find the value of cos (A) = ?

Q: If sin(A+B)=1 and cos(A-B)= V3 -,0B then find A and B

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

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Q: Given z, = 18(cos 175°+i sin 175º ) dan z, = 6(cos 54°+i sin 54°). Find: i. ii.

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