14. (6 points) Use sin(– ) = sin r cos y – cos sin y to evaluate sin ( - 7). BONUS. (8 points) Find all r values in (0,27 that satisfy the following equation. sin cos? Hint: sin?. + cos2 = 1.
Consider the following matrix, As[ cos θ sin θ -L-sin θ cos θ J, for some θ E (-π, π] (a) What is determinant of A? (b) Perform an eigen-decomposition of A (c) What does this matrix do to a vector in R2.
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...
| sin(0) Use the identity matrix to find the inverse of A = l-cos(0) cos(0) sin(0)
Entered Answer Preview Result [e^(-2*1)]*[8*cos((9/5)*1)-14*sin((9/5)*t)] - * (cos(.) – 14 sin(6-)) incorrect The answer above is NOT correct. (1 point) Find y as a function of t if 25y" + 100y + 181y = 0, y(1) = 8, y'(1) = 2. y= e^(-2*t) * (8*cos(9/5*t) -14*sin(9/5*t))
Find sin(a) and cos(B), tan(a) and cot(B), and sec(a) and cSC(B). a 14 B (a) sin(a) and cos() (b) tan(a) and cot(6) (c) sec(a) and csc()
14 and 17 ty Recall that cos bt = (elb + e")/2 and that sin b1 = ( -e )/2i. In each of Problems 11 through 14, find the Laplace transform of the given function; a and b are real constants. Assume that the necessary elementary integration formulas extend to this case. 11. f(1) = sin bt 12. f(t) = cos bt 13. f(t) = eaf sin bt 14. f(t) = el cos bt
de 14) 55+ Acos e sin de 5+ 4 cos e 13) 2 - cos 15) cos 2 de 1-2k cos A + k? < 1)
14. Prove the trigonometric identity: (4) 2) (sin x + cos x)() come an d sin 2x – cas e
2.13 Probiems 73 216 Prove de Moivre's formula (cos θ + j sin θ)" = cos(n θ) + j sin(ne). where n is an integer 217 Use de Moivre's formula, given by Eq. (2.80), to develop the rectangular and polar form representations of the (2.80) following complex numbers: 2.18 Show that 219 Determine the roots of the following second-degree polynomials (a) (G)-2s2 -4s + 10, 2.13 Probiems 73 216 Prove de Moivre's formula (cos θ + j sin θ)" =...