Inverse sine is one of the inverse trigonometric functions of the sine function and it is written as sin-1x and is read as "sin inverse x". Then by the definition of inverse sine, θ = sin-1[ (opposite side) / (hypotenuse) ]
Some values are excluded from the domain and range of trigonometric functions depending upon the region where the trigonometric function is not defined. In this article, we will explore the domain and range of trigonometric functions using table, and graph, and domain and range of inverse trigonome...
Therefore, the domain ofsin−1(x)Is {eq}\left [... Learn more about this topic: Domain & Range of a Function | Definition, Equation & Examples from Chapter 7/ Lesson 3 228K What are the domain and range of a function? What are the domain and range of the graph of a function?
Find the range of f(x)=sin−1x+tan−1x+cos−1x Video SolutionStruggling With Inverse Trigono...? Get Allen’s Free Revision Notes Free ALLEN Notes Text SolutionVerified by Experts Clearly, the domain of the function is [−1,1] Also, tan−1x∈[−π4,π4] for x∈[...
sin2x ≤ 1 sin x ∈ [-1, 1] Hence, we got the range and domain for sine function. Similarly, following the same methodology, 1- cos2x ≥ 0 cos2x ≤1 cos x ∈ [-1,1] Hence, for the trigonometric functions f(x)= sin x and f(x)= cos x, the domain will consist of the ...
The logarithmic function is an inverse function. Recall that in the case ofinverse functions, Let f : A → B be a bijection. Then a function g : B → A which associates each element y∈B to a unique element x∈A such that f ( x ) = y is called the inverse of f. ...
INVERSE TRIGONOMETRIC FUNCTIONS BOOK - RESONANCE DPP ENGLISHCHAPTER - MATRICESEXERCISE - All Questions 7videos MATRICESSimilar Questions The range of the function, f(x)=(1+sec−1x)(1+cos−1x) is View Solution The range of the function f(x)=sec−1(x)+tan−1(x) ,is View Solut...
f(x)=±1−sin2(sin−1(x)) The sine and the inverse sine function cancel; leaving uswith x2 : f(x)=±1−x2;−1≤x≤1 We cannot know whether we use the + or the - signwithout more information regarding the quadrant of the angle. Was this answer help...
Domain:The domain of the functions is the set ℝ (or) (-∞, + ∞). Range:The range of the functions is [-1, 1] Thedomain and range of all trigonometric functionsare shown below: Trigonometric FunctionsDomainRange sin θ(-∞, + ∞)[-1, +1] ...
The inverse function is f^(−1)(x)=sin ^(-1)(x+1)2.To find the range of f, solve y=2sin x−1 for sin x and use the fact that −1≤ sin x≤ 1.y=2 sin x-1sin x=(y+1)2−1≤ (y+1)2≤ 1−2≤ y+1≤ 2−3≤ y≤ 1The range of f is \(y∣ ...