Mathematics, 17.12.2019 07:31 frankiesoar68
The goal of this exercise is to study euler’s important identity e ix = cos(x) + isin(x) and some of its consequences that will be useful in this course. (a) find the real and imaginary parts of the complex number e (2+ π 4 i) . (b) note that e ixe iy = e i(x+y) . use this fact and euler’s identity to rederive trigonometric formulas for sin(x+y) and cos(x+y) in terms of the quantities sin(x), sin(y), cos(x), cos(y). (c) for any a, b ∈ r, show that e (a+bi)x , e(a−bi)x are in the complex span of {e axcos(bx), eaxsin(bx)} by explicitly writing these two functions as complex linear combinations of e axcos(bx) and e axsin(bx). conversely, explain also how you can write each of the functions e axcos(bx), eaxsin(bx) as a complex linear combination of e (a+bi)x , e(a−bi)x . this shows that spanc{e (a+bi)x , e(a−bi)x } = spanc{e axcos(bx), eaxsin(bx)}. (d) consider the quantity bcos(µt)+csin(µt) where b, c, µ are positive real numbers. draw a right angle triangle with side lengths b, c and hypotenuse length a = √ b2 + c2 . let θ be the angle (in radians) between the side of length b and the hypotenuse. solve for b and c as functions of a and θ and use this to rewrite the quantity bcos(µt) + csin(µt) as a function of a, θ, µ, t, i. e., eliminate b and c. finally explain why bcos(µt) + csin(µt) = acos(µt − θ). a is called the amplitude of the final expression and θ is called the phaseshift. this final form of the expression is often called the phase-amplitude
Answers: 2
Mathematics, 21.06.2019 15:00
Δabc is reflected across line l to form δ alblcl, and a¯¯¯al¯¯¯¯ intersects line l at point d. which equation is not necessarily true?
Answers: 3
Mathematics, 21.06.2019 16:00
The table shows values for functions f(x) and g(x) . x f(x)=3x g(x)=2x+1 −2 19 −3 −1 13 −1 0 1 1 1 3 3 2 9 5 what is the solution to f(x)=g(x) ? select each correct answer.
Answers: 1
Mathematics, 21.06.2019 20:00
Three baby penguins and their father were sitting on an iceberg 0.50.50, point, 5 meters above the surface of the water. the father dove down 4.74.74, point, 7 meters from the iceberg into the water to catch dinner for his kids. what is the father penguin's position relative to the surface of the water?
Answers: 2
The goal of this exercise is to study euler’s important identity e ix = cos(x) + isin(x) and some of...
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Social Studies, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Biology, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Chemistry, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01
Mathematics, 16.09.2020 09:01