Which of the following correctly expresses cos(2β)+cos(6β) as a product? −2sin(2β)cos(4β) 2sin(4β)cos(2β) −2sin(4β)sin(2β) 2cos(4β)cos(2β)
2. Prove the following identity. [5] sine+2sin? O cos? 0 + cose=1
USING MATLAB please show all commands (sin x + cos x)^2 = 1 + 2sin xcos x (b) 1 - 2cos x - 3cos^2 x/sin^2 x = 1 - 3cos x/1 - cos x For each part, verify that the identity is correct by calculating the values of the left and right sides of the equation, substituting x=20 degree.
Prove the identity. 4 cos 40 - 4 sin 40 = 4 cos 20 To verify the identity, start with the left side and transform it to obtain the right side. Choose the correct stop and transform the expression according to the step chosen 4 cose-4 sine = 4 cos 20
Prove the Dirichlet Kernel: 1/2 + cos(θ) + cos(2θ) + cos(3θ) + ... + cos(Nθ) = sin[(N+1/2)θ] / 2sin(θ/2) for all θ ≠ 2πn
Use trigonometric identities to solve the equation 2sin(2θ)-2cos(θ)=0 exactly for 0≤θ≤2π. A.) What is 2sin(2θ) in terms of sin(θ)and cos(θ)? B.) After making the substitution from part 1, what is the common factor for the left side of the expression 2sin(2θ)-2cos(θ)=0 ? C.) Choose the correctly factored expression from below. a.) b.) c.) d.) We were unable to transcribe this imageAsin(e) cos(O) = 2cos(e) We were unable to transcribe this imageWe were unable to transcribe this image
let f=cos^2(x)i+yj+z^2sin(x)k. calculate div(f) and curl(f)
Differential Geometry (4) Show that the helix α(t) = (2 cos(3t), 2sin(3t), 3t) lies on a circular cylinder, and find the arc-length of the helix. Determine β(s), the Reparametrized the helix by using the arc-length as the parameter.
Solve for 14(b,c) and 18 (b,c) please 16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the graph of r(t) (e.2 cos(t).2sin(t)) at to-0. Use the qu tion to approximate r(0.1). tion function to find the velocity and position vectors at t 2. 17. Find the principal unit normal vector to tih curve at the specified value of the parameter v(0)-0, r(0)-0 (b) a(t)cos(t)i - sin(t)i (a) r(t)-ti+Ij,t 2 (b) rt)-In(t)+(t+1)j.t2 14. Find the...
solve the exact differential equation (-2sin(x)-ysin(x)+2cos(x))dx+(cos(x))dy=0 where y(0)=5