Verify that tan(2θ) = 2 tan(θ) 1/tan2 (θ)
Verify the identity −ln|sec(θ)−tan(θ)|=ln|sec(θ)+tan(θ)|
A bored teenager who is also good at physics is standing at the top of a hill that is sloping downward by an angle ϕ=0.189 radians.ϕ=0.189 radians. She wants to throw a rock at an angle θ above the horizontal (see the image below) that will maximize the distance the rock travels. What angle θ (in radians) should she go with? Hint: You may find the trigonometric identity tan(2θ)=2tan(θ)1−tan2(θ)tan(2θ)=1−tan2(θ)2tan(θ) useful. hill
Solve the equation in the interval [0°, 360°). 4 sin^2θ = 3 csc θ = 1 + cot θ 3 sin^2θ - sin θ - 4 = 0 2 cos^3θ = cos θ
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
solve the equation on the interval [0,360) 3) 4 tan2 + 7 tan 0 - 2 = 0 4) 3 sin2 x + sin x = 0
12) Find ? tan2 xdx. 12) Find ſ tan” xdx.
Solve the equation in the interval [0°, 360°). sin^2θ - sin θ - 12 = 0 sin 2θ = -sin θ 2 cos2θ + 7 sin θ = 5
Suppose thatX1,...Xn are IID with pdf f(x;θ) = 1 /2θ if -θ<x<θ otherwise =0 (a) Find an unbiased estimator of θ. You must prove that your estimator is unbiased. (b) Find the variance of the estimator in (a).
b. 2. (12 pts.) Find the exact value. sin(1659) c. sin(52.5°) sin(7.5°) tan(159) 1 - tan2(15°) a.