Verified answer

cos x = -1/√2 = -(√2)/2

x = (2k+1)π ± (π/4)

x = -3π/4, -5π/4, 3π/4, 5π/4

in case you have discovered that sin = y/r and cos = x/r, then you certainly would desire to be attentive to that tan = y/x, and for this reason, cot = x/y. then you definately would desire to be attentive to the place x = -a million, y = a million or the place x = a million, y = -a million, to fulfill the incontrovertible fact that cot theta = -a million. this occurs interior the 40 5-40 5-ninety degree triangle, so which you would be able to desire to look at angles the place those 2 situations of x and y happen. x = -a million, y = a million happens interior the 2d quadrant; a 40 5-degree perspective in this quadrant is a hundred thirty five ranges. x = a million, y = -a million happens interior the fourth quadrant; a 40 5-degree perspective in this quadrant is 315 ranges. They repeat each 2 pi, or each 360 ranges. very final answer: Theta = a hundred thirty five + 360n, and Theta = 315 + 360n, the place n is any integer. employing radians, Theta = 3 pi/4 + 2n(pi), and Theta = 7 pi/4 + 2n(pi), the place n is any integer. it could additionally be stated Theta = a hundred thirty five + 180n, or Theta = 3 pi / 4 + n(pi), the place n is any integer, as a results of fact particularly tangent and cotangent repeat each pi or each one hundred eighty ranges. i be attentive to that's multiple cloth, in spite of the incontrovertible fact that it avoids using a calculator. i desire this facilitates.

Let Cos@=1/root2, @=cos^-1(1/root2)=45',as the prinicipal branch of cos^-1 is [0 pi],therefore @=pi/4,or 45'