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Question.4. Find the modulus and argument of sin (θ)-ics() -cos (θ)-i sin (0) COS Given that...
23. What values for θ(0 2π) satisfy the equation? θ 2 sin θ cos θ + cos θ 0
If sin(π/4)=cos(θ) and 0 < θ < π/2, then θ=
Problem 7. (20 pts) A) Find all of the values of θ for which sin θ-1/4. B) Find all of the values of θ for which cos θ-1/4. C) Find all of the values of x for which sin(うー) = 1 /4 D) Find all of the values of z at which the function y -(l m) sinl 2m" -T/3 ) has the value y-^. 2π 2 7T
4 cos(θ)-b , where θ is in Quadrant 1. Use the given information about θ to find the exact values of (a) sin(20) (b) cos(20) (c) tan(20) Preview Preview Preview Points possible: 10 Unlimited attempts.
8. (a) (5pt) Prove the identity: cscx -cos x=sec x . sin'x 4 and tan θ<0 (b) (5pt) Find cos θ , if sin θ
8. (a) (5pt) Prove the identity: cscx -cos x=sec x . sin'x 4 and tan θ
= Let cos(6) sin(0) B - sin() cos() and 0 << 27 (i) Calculate the eigenvalues of B. Hence prove that the modulus of the eigenvalues is equal to one. (ii) Calculate the eigenvectors of B.
Time series analysis
1. (a) Use Euler's identity e¡θ-cos θ + i sin θ to prove that sin θ=-(eiO , 2i (b) Use the identities above and the formula for the sum of a geometric series to prove that if n is an integer and j E 1,2,... ,n} then TL TL sin-(2Ttj/n)- n/2 so long as J关[m/2, where Laj is the greatest integer that is smaller than or equal to x (c) Show that when j 0 we have...
An ellipsoid, S, is parameterised by r = a sin θ cos
φi + a sin θ sin
φj + b cos θk 0
≤ θ ≤ π 0 ≤ φ ≤ 2π
i. Find the surface element dS, such that
dS points OUT of the ellipsoid.
ii. Hence determine the following surface integral over the
ellipsoid:
//rds JJs
Question 5 Given arcsin (9/20) find cos () Question 6 Given sin 4x+sin 6x=0 Find the solution that corresponds to the positive k=1 solution for the sine part. Question 7 Given sin 5x-sin 4-0 MacBook Air
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