V2/2 u (d) Using the identity V2 – (V2 sin 0)2 = V2cos 0 when cos...
[6] sin 2B given sec B - 3 cos 2B and & sin >0. In what quadrant does 2B terminate? 7 5 [7] Verify the identity: 2 csc A sin A 1 + cos A + 1 + cos A sin A
State the quadrant in which lies. sin(8) <0, cos(8) < 0 OII III OIV 8 If sin() and 8 is in the 1st quadrant, find the exact value for cos(8). 9 cos(8) - > Next Question State the quadrant in which lies. tan(8) > 0, csc(8) < 0 01 OII O III OIV
Using the identity sin? 0 + cos² 0 = 1, find the value of tan 6, to the nearest hundredth, if sin 0 = -0.62 and 3 < 0 < 27.
Evaluate the following integral using residues: cos(bx)-cos(ax) I = dx. x2 Let a and b: real constants such that a > b >0. Note: cos(bz)-cos(az) has a singularity at z = 0 is removable, z2 ejbz-ejaz has a pole at the origin. Make sure to handle this point correctly 22
Use induction and Pascal's identity to prove that (7) = 2" where n > 0.
T Find the length of the curve e' cos(t) e' sin(t) for 0 < t < 2 y (Hint: You can simplify the integrand by expanding the argument inside the square root and applying the Pythagorean identity, sinº (0) + cos²O) = 1.)
TT If sin sin (m) cos(0) and 0° < 2. t then 2 =
= 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.
Write the expression as an algebraic (nontrigonometric) expression in u, u> 0. cos (arctanu) cos (arctan u) = 0 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) The following function approximates the average monthly temperature y (in °F) in a city. Here x represents the month, where x= 1 corresponds to January, x=2 corresponds to February, and so on. Complete parts (a) (b). flx) = 11 sin [«- 49]+50...
Use a trigonometric identity to find exactly all solutions: cos 20 = sin , 0<o<21. Enter the exact answers in increasing order. O= Edit 6 31 Edit 2 II 5a 6 Edit