Webbvalue branch of the function cos–1. We write cos–1: [–1, 1] → [0, π]. The graph of the function given by y = cos–1 x can be drawn in the same way as discussed about the graph of y = sin–1 x. The graphs of y = cos x and y = cos–1x are given in Fig 2.2 (i) and (ii). Fig 2.2 (ii) Let us now discuss cosec –1x and sec x as follows ... Webb23 juni 2024 · Jun 23, 2024 at 17:50. A logarithm of a complex number w ≠ 0 is a complex number z such that e z = w. When w ∉ ( − ∞, 0], we call principal value of the logarithm of w to the only logarithm whose imaginary part is in ( − π, π). In other words, among all logarithms of w, we pick the only logarithm z of the form with b = (.
Class 12 NCERT Solutions – Mathematics Part I - GeeksforGeeks
WebbThese conventions are outlined in section 2.2.5 of ref. 2. The principal value of a multi-valued complex function f(z) of the complex vari-able z, which we denote by F(z), ... We conclude that Arccot z must be discontinuous when z = x + iy crosses the branch cut located on the imaginary axis such that x = 0 and −1 < y < 1. Webb30 mars 2024 · Ex 2.1, 7 Find the principal value of sec−1 (2/√3) Let y = sec−1 (2/√3) sec y = 2/√3 sec y = sec (𝝅/𝟔) ∴ y = 𝝅/𝟔 Since Range of sec−1 is [0, π] – {𝜋/2} Hence, Principal Value is 𝝅/𝟔 (Since sec 𝜋/6 = 2/√3) Next: Ex 2.1, 8 Important → Ask a doubt Chapter 2 Class 12 Inverse Trigonometric Functions Serial order wise Ex 2.1 ray wolfe construction
Ex 2.1, 7 - Find principal value of sec-1 (2/root 3) - Chapter 2
WebbPrincipal value branch of sec-1 x is . Question 6. Write down the interval for the principal-value branch of each of the following functions and draw its graph: cosec-1 x. Answer: Principal value branch of cosec-1 x is . Objective Questions Question 1. Mark the tick against the correct answer in the following: WebbInverse Trigonometric Functions Problems. Example 1: Find the value of x, for sin (x) = 2. Solution: Given: sin x = 2. x =sin -1 (2), which is not possible. Hence, there is no value of x for which sin x = 2; since the domain of sin -1 x is -1 to 1 for the values of x. Example 2: Find the value of sin-1(sin (π/6)). Solution: WebbAgain, if the principal value of sec − 1 x is α (0 < α < π) and α ≠ π 2 then its general value = 2nπ ± α, where, x ≥ 1. Therefore, sec − 1 x = 2nπ ± α, where, (0 ≤ α ≤ π), x ≥ 1 and α ≠ … ray wolf nz