## Guest

Bidhan
12 Points
5 years ago
Let`s consider sinx=Z, now let`s critically observe the value of x and Z.... The value of Z should lie in between - 1and +1....now the value of x should be between 0 and 1.57(??) (((as x=pi/2=1.57)))).so obviously if sin inverse x>Z, then x>sin..... And we should remember ur question should have the condition as x
Vaibhav Singh
57 Points
5 years ago
Dear Piyush, in inverse trigonometric functions there are certain range and domains in which the function is defined unlike simple trigonometric functions. Otherwise they contradict basic property of a function (one value for one point). For example Sin-1 has range [-pi/2 , pi/2] and domain [-1, 1] and Cos-1 has range [0,pi] and domain [-1 , 1].In this domain Cos-1 is decreasing therefore if Cos-1x > p. Then x p. Then, x > Sinp. Please approve this answer if it cleared your query.
Arun
25758 Points
5 years ago
hey piyush,
just observe the graph of sinx & cosx
we see that sinx is increasing function that means on increasing the value of x, sinx will increase
while on the opposite side, cosx is a decresing function that means if we increase x, cosx will decrease

now using this if  cos-1x > 2/3,  x

but in the case of sin, if sin-1x > 2/3,  x>sin2/3
Hope it clears