Find the exact value of the expression(Consider interval is [0,pi]
1) sin^-1 SQRT3 / 2 = pi/3
2) arctan(-1) = 3pi / 4
3) csc^-1 2 = pi/6
4) sec^-1 SQRT(2) = pi/4
II) We were given the example to derive sin^-1x as follows.
siny = x
(cosy)(dy/dx) = 1
(dy/dx) = 1/cosy = 1 / (SQRT(1-sin^2 (y))
= 1 / SQRT(1-x^2) (-pi/2 < y < pi/2)
NOW, please follow the same steps, but now derive cos^-1 (x) and then cot^-1 (x).
Here are the solutions to the problems given.
1) As we know that sin60 = sqrt(3/2) = sin(pi/3)
Substituting the value of sqrt(3/2)
Left Hand Side = sin^-1sin(pi/3)
2) We know that tan(3pi/4) = -1 = ...
The solution gives a step by step procedure to solve a couple of problems related to inverse functions.