1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Molodets [167]
3 years ago
8

Using Euler's relation, derive the following relationships:a. Cosθ=½(e^jθ+e^−jθ)b. Sinθ=½(e^jθ−e(^−jθ)

Mathematics
1 answer:
Montano1993 [528]3 years ago
4 0

Answer:

a. cosθ = ¹/₂[e^jθ + e^(-jθ)] b. sinθ = ¹/₂[e^jθ - e^(-jθ)]

Step-by-step explanation:

a.We know that

e^jθ = cosθ + jsinθ and

e^(-jθ) = cosθ - jsinθ

Adding both equations, we have

e^jθ = cosθ + jsinθ

+

e^(-jθ) = cosθ - jsinθ

e^jθ + e^(-jθ) = cosθ + cosθ + jsinθ - jsinθ

Simplifying, we have

e^jθ + e^(-jθ) = 2cosθ

dividing through by 2 we have

cosθ = ¹/₂[e^jθ + e^(-jθ)]

b. We know that

e^jθ = cosθ + jsinθ and

e^(-jθ) = cosθ - jsinθ

Subtracting both equations, we have

e^jθ = cosθ + jsinθ

-

e^(-jθ) = cosθ - jsinθ

e^jθ + e^(-jθ) = cosθ - cosθ + jsinθ - (-jsinθ)

Simplifying, we have

e^jθ - e^(-jθ) = 2jsinθ

dividing through by 2 we have

sinθ = ¹/₂[e^jθ - e^(-jθ)]

You might be interested in
Katy is older than Alex and Beth. Sarn is
Sholpan [36]
This would be Delores because it goes katy, Delores, Alex, Sam, Beth
8 0
3 years ago
A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y=ax2 about the y-a
Blizzard [7]

Answer:

Step-by-step explanation:

See attached file .

7 0
3 years ago
HELP ASAP!!! ILL GIVE LOTS OF POINTS AND BRAINLIST<br><br> PLEASE SHOW HOW YOU GOT THE ANSWER!
Kruka [31]

Answer: 27

Step-by-step explanation:

7 0
2 years ago
Steven wishes to save for his retirement by depositing $2,000 at the beginning of each year for thirty years. Exactly one year a
Ad libitum [116K]

Step-by-step explanation:

i = interest 3% for 30 years

This is a simple dynamical system for whom the the solutions are given as

S=R[\frac{(i+1)^n-1}{i}](i+1)

putting values we get

S=2000[\frac{(1.03)^{30}-1}{0.03}](1.03)

= $98005.35

withdrawal of money takes place from one year after last payment

To determine the result we use the present value formula of an annuity date

P = R\frac{1-(1+i)^{-n}}{i}{i+1}

we need to calculate R so putting the values and solving for R we get

R= $6542.2356

8 0
3 years ago
If f(x) = 2x + 6 and g(x) = -4x - 8 find f(g(x)) = ?x+?
amm1812

hope it helps

plz mark brainliest

6 0
3 years ago
Other questions:
  • -5x+y=-3
    10·1 answer
  • Hannah bought 4 hamburgers and 2 orders of French fries at for $16.50. Phillip bought 5 hamburgers and 3 orders of French fries
    11·1 answer
  • Help plz plz plz i need help, not good at math
    11·1 answer
  • 1. Find the sum of the series . 15 show your work
    5·2 answers
  • -2.8 f +0.9 f - 12 - 4
    7·2 answers
  • PLEASE HELP ME.!!!!! <br> I’m begging you
    14·1 answer
  • Simplify: 121/11 + 3(4)/2<br> Please and thank you. :)
    9·1 answer
  • 2x-y=-4 what is the zero of x-intercept graphically ​
    9·1 answer
  • Help on this please
    8·2 answers
  • Which conclusions are valid given that ABCD is a parallelogram? Select True or False for each statement.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!