2. In this problem, you will prove the sin and cos sum formulas in two ways. sin(a + b) = sin a cos b + cos a sin b cos(a + b) = cos a cos b – sin a sin b • Use Euler's formula: e’a = cos a + i sin a to prove the formulas. • Use the rotation matrix Ro from last term and the fact that the matrix of a com- position of two linear transformations is the product of their respective matrices. (therefore R9R,: = Ro+v)

Q: Transform triangle ABC with vertices A (4,0), B(0, 2), and C(-2, -1) as shown. RO. 1800(ABC) A'. В'…

A:

Q: Question 12 Compute the orthogonal projection of u onto v. Use the square root symbol 'V' where…

A:

Q: Show that the matrix is invertible and find its inverse. 9] A-1 = A = sin 8 [₁ cos Ꮎ -cos 0 sin 0

A:

Q: Compute the Jacobian at the indicated point. G(r, t) = (r sin (t), r – cos (t)), (r, t) = ( 6,…

A: Jacobian of the function at a given point

Q: dw = t³ and y = 7. Find dt Let w = cos(8x - 10y), where x =

A:

Q: Jo cos*0 d0 T/2 3. sin'e cos°0 de 5. sin°(21) cos (21) dt 7/2 7. cos 0 de

A:

Q: Problem 1: Express the complex function w = x² – y² – 2y + (2x – 2xy)i in terms of z = x + iy and z…

A: w = x2 - y2 - 2y + (2x - 2xy)i Hence, w = (x2 - y2 -2xyi) + 2xi - 2y = (x2 - y2 - 2xyi) + 2xi +…

Q: The matrix that rotates the x-y plane by an angle is [cos - sin 0 A(0) cos Ꮎ sin 0 1(0₁)A(0₁₂) = A…

A: Introduction: If the number of columns in A equals the number of rows in B, then A and B's product…

Q: tation by an angle 0 can be written in matrix form as: [cos(0) - sin(0)] sin(0) cos(0) Use this and…

A: For this we may take two figures as follows:

Q: The complex numbers Z₁ and Z₂ are defined as follows: ²1 6 (cos(4) + i sin(4T)) = Z₂ Calculate = 12…

A: The given complex numbers are…