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: 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:
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Webbis known as the principal value branch of the function y = cot–1 x and these values of are known as they principal values. 5. Inverse secant function Consider the function f defined by f (x) = sec x, D f = R except odd multiples of π 2 and R f = (–∞, – 1] ∪ [1, ∞). A portion of the graph of sec is shown inx fig. 5.10. WebbLearn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the …
WebbEconomics (/ ˌ ɛ k ə ˈ n ɒ m ɪ k s, ˌ iː k ə-/) is a social science that studies the production, distribution, and consumption of goods and services.. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes what's viewed as basic elements in the economy, including individual agents and … 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 ...
WebbSec Inverse x is the inverse trigonometric function of the secant function.Mathematically, it is denoted by sec-1 x. It can also be written as arcsec x. In a right-angled triangle, the secant function is given by the ratio of the hypotenuse and the base, that is, sec θ = Hypotenuse/Base = x (say).Using this, sec inverse x formula is given by θ = sec-1 x = sec … WebbSince the range of principal value branch of y= cosec-1 x is [- π/2 , π/2] \ {0} and. Thus, the principal value of cosec-1 (-1) is – π/2 . (ii) Let y = sec-1 ... [0, π ] \ {π/2 } , the principal value of sec-1 (-2) is 2π/3 . Example 4.13. Find the value of sec-1 (- 2√3 / 2) Solution . Example 4.14. If cot-1 ( 1/7 ) = θ , find the ...
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
WebbThus the principal value of csc-1 (-1) is -π/2. Problem 10 : Find the principal value of sec-1 (-2). Solution : Let y = sec-1 (-2). Then, sec y = -2. The range of principal value branch of y = sec-1 x is [0, π] \ {π/2} Let us find y in [0, π] - {π/2} such that sec y = -2. But, sec y = -2 -----> cos y = -1/2. Now, in a rare instanceWebbWhich of the following is the principal value branch of cosec 1 x ?a π/2, π/2b [0, π] π/2c [π/2, π/2]d [ π/2, π/2] [0] Login. Study Materials. NCERT Solutions. NCERT Solutions For … in a rareWebbI can't understand why $1/x$ can have a principal value because it's not a multivalued function ... which is for selecting single-valued branches of multi-valued functions. I know, it's stupid. You'd think someone would have ... See Saff, Snider Fundamentals of Complex Analysis, Section 8.5 Question 8. The third one is the Kramers-Kronig ... in a rash manner definitionWebbThe value of limit x→pi/2tan^2x (√ (2sin^2x+3sinx+4)-√ (sin^2x+6sinx+2)) is equal to: Class 11 >> Applied Mathematics >> Limits and Continuity >> Methods of evaluating limit of a … in a rare form of deceptionWebbWhat is the principal value branch of sec –1 x ? 29 \left[0\ ,\ \pi\right]-\left\{\frac{\pi}{2}\right\} (–1, 1) [0, \pi] [–1, 1] Solo games Try one here Simple quiz Preview as a student. Edit a copy to suit your class. Our brand new solo games combine with your quiz, on the same screen. duth originals - smartwatchWebbDifferentiate sec (x )22 with respect to x2. Ans: Let x2 = u, differentiating sec2u w.r.t u, putting u = x2 1/2 2sec x tan x22 2 1/2 OR If yf(x)= 2 and f(x) e′=x, then find dy dx. Ans: ()2 x dy 'x 2x dx = 2xe =f 1/2 17. Find the value of k, so that the function kx 5, if x 12 f(x) 2,ifx1 ⎧⎪ + ≤ =⎨ ⎪⎩ > is continuous at x = 1. Ans ... duth netWebby = sec − 1 x x = sec y Here, x ≥ 1 o r x ≤ 1 The domain includes all numbers from − ∞ to ∞ except the numbers between -1 and 1 ∴ Range of sec − 1 x is all the angles between 0 & 1 8 0 ° except for 9 0 ° ∴ Range = [0, Π] − [2 Π ] in a rare green place d2