1. since cscØ = 1/sinØ
if sin Ø = 0 , the cscØ = 1/0
since we cannot divide by zero, and 1/0 is undefined
csc 0 is undefined
Here is a graph of y = csc x for about 4 periods
the vertical lines are asymptotes, and shows where the cscx is undefined. the sine curve is super-imposed. notice that cscx is undefined when sinx = 0
http://www.wolframalpha.com/input/?i=plot+y+%3D+csc%28x%29+%2C+y+%3D+sinx+%2C+-13%3Cx%3C13
how neat is that ?
2. cos(Ø + π/2)
= cosØcosπ/2 - sinØsinπ/2
= cosØ x (0) - sinØ x (1)
= -sinxØ
1. The expression sinπ is equal to 0, while the expression 1/cscπ is undefined. Why is sinø=1/cscø still an identity?
2. Prove cos(ø + π/2)= - sin ø
1 answer