# What does #2sin(arccos(3))+csc(arcsin(5))# equal?

##### 1 Answer

Undefined if dealing with Real

However, if we use Complex

#2 sin(arccos(3)) + csc(arcsin(5)) = 4 sqrt(2) i + 1/5#

#### Explanation:

If we are talking about Real valued trig functions of Real values, then both

However, it is possible to define

#cos(z) = (e^(iz)+e^(-iz))/2#

#sin(z) = (e^(iz)-e^(-iz))/(2i)#

If

These definitions can be used to calculate

We find:

#2 sin(arccos(3)) = 2 sqrt(1-3^2) = 2 sqrt(-8) = 4sqrt(2) i#

#csc(arcsin(5)) = 1/sin(arcsin(5)) = 1/5#

So:

#2 sin(arccos(3)) + csc(arcsin(5)) = 4 sqrt(2) i + 1/5#