Show that w = 2(cos 15° + i sin 15°) is a fourth root of z = 8 + 8iy3 by raising w to the fourth power and simplifying to get z. (The number w is a fourth root of z, w = z!/4, if the fourth power of w is z, wA = z.)

Q: Find the cartesian equation of the following: 6 1. r = 3-sin 0 2. r2 cos(20) = 4 %3D 9. 3. 4 sin(20)…

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Q: 7. Find the maximum and minimum values of the expression 2 cos 0-4sin 0. Hence, determine the angles…

A: Given: The expression is: 2 cos θ-4 sin θ Find the maximum and minimum values of the given…

Q: If sin(8) = 3 and 0 is in the 1st quadrant, find cos(0) 8. cos(0) = Enter your answer as a reduced…

A: Answer is given in next step.

Q: Use Euler's formula and find real and imaginary part of: Z1 = sin(1– 3i) 22 = cos(3+ 2i)

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Q: True or False The set of all solutions of the equation tan 0 = 1 is given by {o0 = + ka, k is any…

A: To find the solution of tan θ = 1 => (sin θ)/(cos θ) = 1 => sin θ = cos θ This is possible…

Q: Determine whether the positive or negative square root should be selected. 1+ cos 220" cos 110.0° =+…

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Q: 5 7. Given that sin 0 and 270° < 0 < 360°, sketch 0 in standard position and fin 13 sin 2 а.

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Q: Verify the given sum-to-product formula cos * + cos * = 2cos [(* + *)/2] cos * - */2}. Start with…

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Q: 2п 2п 3. Find the fourth roots of 16 [cos(3 Hisin(). 3

A: Solution:-

Q: Express in the form a + bi where a and b are real numbers.

A: we have z = 12cos4π3+ isin4π3    Now 4π3= π+π3 hence z = 12cosπ+π3+ isinπ+π3               =…

Q: [3(cos 18° + i sin 18°). [2(cos 20° + i sin 20°)]³.

A: De Moivre's Theorem: cosθ+isinθn=cosnθ+isinnθ where n∈ℤ

Q: Find the product of z1 & Z2, leave answer in trigonometric form: 235 (cos플 + isin) & z2 =: +i sin 3…

A: We know that for  z1 = r1 cos θ1 + i sin θ1  and  z2 = r2 cos θ2 + i sin θ2 z1·z2 = r1·r2 cosθ1+θ2 +…

Q: Express in the form a + bi where a and b are real numbers.

A: To express: The expression 3cos3π2+isin3π2 in the form of a+ib. Given: The expression is…

Q: 10. Find all solutions to: sin(30) = cos(60) %3D in [0°, 360°). DO NOT ROUND - exact answers only.

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Q: Find the four fourth roots of z = 625( cos + i sin 3 Write each root in standard form. 3

A: To find four fourth roots ofz=625(cos2π3+isin2π3)

Q: Find the fourth roots of z= 16(cos 60 + i sin 60)

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Q: find the exact value of cos 227 cos 167 + sin 227 sin 167 by using the formula for cos (a-b).

A: Solution :       We have to find the exact value by using the formula for cos(a - b)  = ? Now, Given…

Q: 3. Find all solutions of the given equations. a. tan 0 + cot 0 = 4 sin 20 b. sin 20 =3 cos 20

A: According to question given that (a) tanθ + cotθ=4 sin 2θ(b) sin 2θ=3 cos 2θ

Q: State whether the following statement is true or false. Explain. 5T sin 8. 元 元 5 cos - + i sin 8. •…

A: Given:     5cosπ8+isinπ8·2cosπ2+isinπ2=10cos5π8-isin5π8   Solving the left side of equation…

Q: Express the number –9 in the form R(cos(0) + i sin(0)) = Rei where R0 and 0 ≤ 0 ≤ 2π. NOTE: Enter…

A: Solution :  Given  number   - 9

Q: 4. Find the exact value of cos(83°) cos(23°) + sin(83°) sin(23⁰)

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find the four fourth roots of z = 81 (cos 4? /3 + i sin 4? /3) . Write each root in standard form.

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Q: Find all solutions to cos(80) – cos(20) = sin(50) on 0 <0 < 3 0 = 0, Give your answers as a list…

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Q: O Find all sixth roots of z = 64 (cos 120° + i sin 120°). Leave your answer in Trigonometric Form

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Q: 5. Is the equation cos 8- sin 0 =1 an identity? If so, verify it. If not, explain why.

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Q: Find all angles, 0° <0< 360°, that satisfy the equation below. 9 cos (0) – 2 sin(8) – 9 = 6 sin(0) –…

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Q: Find all solutions to cos(70) cos(p) = sin(40) on 0 ≤ ø Give your answers as a list separated by…

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Q: Find all solutions to cos(7ø) – cos(4) sin(4ø) on 0 < ¢ < 3 Give your answers as a list separated by…

A: cos(7ϕ)-cos(ϕ)=sin(4ϕ)-2sin7ϕ+ϕ2sin7ϕ-ϕ2=sin(4ϕ)-2sin(4ϕ)sin(3ϕ)=sin(4ϕ)sin(4ϕ)+2sin(4ϕ)sin(3ϕ)=0sin…

Q: Find the three cube roots of 8(cos 264° +j sin 264") and state which of them is the principal cube…

A: Given - 8cos 264° + jsin 264° To find - Find the three cube roots of 8cos 264° + jsin 264° and state…

Q: considering only the values of θ for which sec^2θcos(2θ) is defined, sec^2θcos(2θ)= ?

A: SecA=1/cosA Cos2A=2cos2A-1

Q: 8. a. Verify the given identity: sec(0)- cos(0) = sin(0))tan(0) b. Use part a to solve the equation:…

A: (a) given as sec θ- cos θ= sin θ tan θ Simplify left-hand side as sec θ- cos θ= 1cos θ-cos…

Q: Find all the values of theta, if theta is in the interval (0,360 degrees) and has the given function…

A: We need to solve sinx=32. So,              sinx=32⇒x=π3+2πn, x=2π3+2πn

Q: 4

A: Recall the following double angle formulas:

Q: Find all solutions to cos(5ø) – cos(4) = sin(3ø) on 0 < ¢ < T $ = Give your answers as a list…

A: To find the all solutions for the given trigonometric equation.

Q: The terminal side of an angle e in standard position contains the point (3, 12). Select all of the…

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Q: 3. Express M =cos 3A+cos A and N = sin 3A+sin A as a product form. M = cot 2A. N Hence, show that

A: topic- trigonometry

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: 8. 15 Use the figure above to find the exact value of sin 20, cos 20, tan 20. sin 20= cos 20= tan…

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Q: 5.1 Prove, without the use of a calculator that: cos75° + cos15º = √6/2

A: To prove without the use of a calculator that, cos75°+cos15°=62

Q: Find the exact value.. 1. Cos 70°cos40°+sin70°sin40° 2. Sin 7π/12 using the fact the 7π/12= π/3 +π/4

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Q: 12 Determine the exact value of sin 20 given that cos=- and 13 3π 2 π<0< without determining the…

A: Concept: Trigonometric ratios: sinθ=PH; cosθ=BH Where P is perpendicular , H is hypotenuse and B is…

Q: Find the solution(s) for theta. 6√3-9 sin 8

A: To solve the given trigonometric equation

Q: Find the three cube roots r1, r2 and r3 of 8(cos 264° + j sin 264°). Express all arguments in…

A: We have to find out cube root of unity for given complex number.

Q: Find sin(2θ), if cosθ=24/25 and θ lies inquadrant IV.

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Q: Given that sinθ= 3/5 and cos(θ)<0 that , what is the exact value of sec(θ)

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Q: Find all values of 0, 0° < 0 < 360°, that satisfy 5 cos 20 + 7 sin 0+1 = 0

A: 5cos2x+7sinx+1=0REwriting we get:6-10sin2x+7sinx=0sinx=-12, sinx=65Combine all the…

Q: Use the given information sec α = -3, π/2 &lt; α &lt; π to find the exact value of the following: a.…

A: Given:             sec α = -3,            π/2 &lt; α &lt; π        cos α = =1sec…

Q: Find all solutions to cos(3ø) – cos(4) = sin(26) on 0<p<2π $ = Give your answers as a list separated…

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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