5)Use De Moivre's theorem to simplify the following a)(cos 20+i sin 20)(cos 50+i sin 50)

Q: cos 30° + sin 60° V3 Prove that 1+ cos 60° + sin 30° 2.

A: Given to prove : cos30∘+sin60∘1+cos60∘+sin30∘=32…

Q: If sino + sin'0 +sin' 0 = 1, then prove that cos 0-4 cos* 0+8cos 0 = 4.

A: sin2 x + cos2 x = 1.

Q: 9. What is Sin(210 deg)= %3D always check if the answer should be positive or negative. *

A:

Q: 8. Use the given information to find sin 20, cos 20, tan 20. sin =.0 < 0 <; %3D

A: Some Trigonometric formula,                             1.   sin2θ+cos2θ=12.   sin2θ = 2sinθcosθ3.…

Q: 1. Use de Moivre's theorem to express sin50 in terms of powers of sin.

A:

Q: Prove the ff Trigonometric Identities: 2. (1- cos²0) csc=0 = 1 3. sect V(1– sin²0) = 1

A:

Q: 1. Prove cos 8-sin 8 cos 8 + sin e = sec 28 tan 20.

A:

Q: Question 7: Use De Moivre's Theorem to (7.4) express cos³0 sin* in terms of multiple angles.

A:

Q: 3. sin 27° =cos ? cos 73° cos 153° cos 27° cos 63° O O O O

A: To find equivalent of sin27

Q: how that cos 1+cos 8 and sin 1-Cos 0 %3D %3D using de Moivre's Theorem.

A: It is required to show that cosθ2=1+cosθ2 and sinθ2=1-cosθ2 by using de Moivre's theorem. By de…

Q: Express the number 8√3-6i in the form R(cos(0) + i sin(0)) = Re, where R> 0 and - ≤ ≤T. NOTE: Round…

A:

Q: Use De Moivre's Theorem to raise the indicated powers. [5 (cos16° + i sin16°)] ^-4

A: We have given a complex number ,  z = 5 cos 16° + i sin 16°-4 We know that , DeMoivre's theorem ,…

Q: (a) (i) Use de Moivre's theorem to express cos 40 and sin 40 in terms of cos 0 and sin 0. 4 tan3 0 4…

A: Expand the expression:  x+iy4=x4+4ix3y-6x2y2-4ixy3+y4=x4-6x2y2+y4+4x3y-4xy3i Set x=cosθ and y=sinθ…

Q: True or False sin ( 20) has two equivalent forms: 2 sin 0 cos 0 and sin² 0 – cos 0

A: Given statement is, sin2θ has two equivalent forms: 2sinθcosθ and sin2θ-cos2θ.   The objective is to…

Q: 125 cos- j sin 11 11 1. Simplify 4т Express answer in rectangular form. 5 cos + jsin 11 11

A:

Q: Part 3 of 4 COS X d —CSC X + С dx To check for the result, prove that 1 - cos?x

A:

Q: Show that V2 + V2 cos 2 and cos 16 and use it to find sin 16 Show that

A:

Q: 15. Find sec0, given that sin 0 2 ,and 0 is in QIII. 5/21 21 d.- а.- 21 21 5 16. Find cos e using…

A: Use trigonometric identity to find value

Q: Find 2 angles (rounded to the nearest 10th of a degree)in the interval [0, 360ﾟ) that satisfy Cos…

A:

Q: Find the value of 2 sin2 30° tan 60° – 3 cos2 60° sec2 30°

A:

Q: 9. (6 points) Verify the following identity. sin 0 cot 0 + csc 0 1+ Cos 0

A:

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: prove that: a- cos20 = cos²0 – sin²0 %3D sin20 = 2sin0cos

A:

Q: 10) Evaluate using Cofunction Identities 2 Cos? 60° - Sec 150° + cot2 30°

A: NOTE: Refresh your page if you can't see any equations. .

Q: Prove 4 (cos 10° + sin' 20° = 3 (cos 10° + sin 20°

A:

Q: Prove that cos 17° + sin17° tan62° %3D cos17° – sin17°

A: Devide the whole left side by Cos17° and use formula of tan(a+b)

Q: Show that sin , +sin ¤, = 2 cos[;(4, – Þ,)]sin[;(P, +Ð,)]

A:

Q: By equating the real parts of cos 5? + ? sin 5? = (cos ? + ? sin ? )5 show that cos 5? = 16cos5?…

A: De-moivre's Theorem, cosθ+isinθn=cosnθ+i sinnθ. For n=5, cosθ+isinθ5=cos5θ+i sin5θ. Simplify LHS as…

Q: 12 and 0 is in QIV. 5. Given: tan 0 What is the value of sin(26)?

A: Topic:- trigonometry ratios

Q: 6. Caleulate v2(cos polar form with the argument from 0 < 0 < 2ñ. 4 COS and express the answer in…

A: r(cosθ+ i sinθ)n=rn(cos(nθ)+ i sin(nθ))

Q: 7. Prove the identity. 1-cos 20 tan 0 %3D sin 20

A:

Q: 3. Find the value of cote + co sece 5. If cos e = %3D

A:

Q: 11 |- tan 20 Cos 20 %3D

A:

Q: Select all the true equations. O cos(15) = sin(15) O cos(75) = sin(15) %3D O cos(75) = cos(15) O…

A: Use trigonometric angle conversion

Q: Determine whether the statement is true or false. cos(30°+45°) = cos 30° ∙ cos 45°- sin 30° ∙ sin…

A:

Q: Find the exact value of cos^-1(sin (7π/6))  show work

A: cos-1(sin7π6)nowsin7π6=-12

Q: 2) Explain why sin(8) = cos(90-e). %3D

A:

Q: If sin theta + 2  cos theta = 1  then prove that 2sin theta - cos theta = 2

A: To Determine: To prove 2sinθ-cosθ=2 Given: we have sinθ+2cosθ=1 Explanation: we have…

Q: Express as funetiou trigonmetric angle. of one * ° ° Cos 45 coss22 +sin45°sin22

A:

Q: cos 30° + sin 60° V3 Prove that 1+ cos 60° + sin 30°

A: Trignometric ratios are

Q: sin 61° = cos ; cos 17° = sin 0;

A: Given: sin61°=cosθ;cos17°=sinθ

Q: What is the simplified form of cos 10r-cos 4x sin 10x+sin 4x O -cot(7x) O -tan(7x) O tan(7x) O no…

A: SOLUTION-

Q: 17 prove 4 Cos" ☺ - Sin" 0 = Cos20

A:

Q: What is the simplified form of cos 10z-cos 42 , sin 102+sin 4æ O -tan(7x) O -cot(7x) O tan(7x) O…

A: We will evaluate the given form to simplest form as shown below

Q: Suppose, for some angle 0 drawn in standard position, tan(e) = -24/7 and sin(0) < 0. Find the exact…

A:

Q: tan 45, sec 60 5 sin 90 sin 60° 2 cos 0 cos135° Leave your answer in exact form (no decimals). 11.…

A: We will directly out the values of all of these then calculate.

Q: (), tan (;). 4. Find sin given that sec(0) = 2, where 90° < 0 < 180° COS

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.