WebWe have six main inverse trigonometric functions, namely inverse sine, inverse cosine, inverse tangent, inverse cotangent, inverse secant, and inverse cosecant. Now, we will explore their antiderivative rules of these trigonometric functions as follows: ∫sin -1 x dx = x sin -1 x + √ (1 - x 2) + C ∫cos -1 x dx = x cos -1 x - √ (1 - x 2) + C WebDEFINITION: The inverse secant function, denoted by sec 1 x (or arcsecx), is de ned to be the inverse of the restricted secant function secx; x 2 [0;ˇ=2)[[ˇ;3ˇ=2) or x 2 [0;ˇ=2)[(ˇ=2;ˇ] in some other textbooks DEFINITION: The inverse cosecant function, denoted by csc 1 x (or arccscx), is de ned to be the inverse of the restricted cosecant function
How do you evaluate csc^-1(sqrt2)? Socratic
WebJun 24, 2016 · Since csc(x) and csc−1(x) are inverse functions, this means that csc(θ) = √2. Another way of reaching that fact is to take the cosecant of both sides: csc(θ) = csc(csc−1(√2)), and since csc(csc−1(x)) = x, this becomes csc(θ) = √2. Taking the reciprocal of both sides, the equation becomes sin(θ) = 1 √2 = √2 2. WebTake the inverse cosecant of both sides of the equation to extract x x from inside the cosecant. x = arccsc( 2√3 3) x = arccsc ( 2 3 3) Simplify the right side. Tap for more steps... x = π 3 x = π 3 The cosecant function is positive in the first and second quadrants. how to trim beautyberry bush
2.2: Graphs of the Secant and Cosecant Functions
WebJul 28, 2015 · Explanation: csc−1( − 7 3) is a number between − π 2 and π 2 whose cosecant is − 7 3 ). That means the sine is − 3 7. csc−1( − 7 3) = sin−1( − 3 7). In general, because cscθ = 1 sinθ, we have: csc−1x = sin−1( 1 x) Note: we use a similar idea to find inverse secant and inverse cotangent on many calculators. sec−1x = cos−1( 1 x) and WebMay 28, 2024 · Vertical and phase shifts may be applied to the cosecant function in the same way as for the secant and other functions.The equations become the following. y = A sec ( B x − C) + D y = A csc ( B x − C) + D FEATURES OF THE GRAPH OF Y = A sec ( B x − C) + D The stretching factor is A . The period is 2 π B . http://www.mathwords.com/c/cosecant_inverse.htm how to trim beard when growing out