dont understand

Question

indentify the intereval(s) on [0,2π] for which the sine function is increasing and cosine function increasing

Answer 1

From the graph of y = sinx, we see that the function is increasing from 0 to π/2 and from 3π/2 to 2π.

 

From the graph of y = cosx, we see that the function is increasing from π to 2π.

 

So, both functions increase from 3π/2 to 2π.  On that interval,       y = sinx increases from -1 to 0 while y = cosx increases from 0 to 1.   

Answer 2

The sine function increases in [0,π/2] ∪ [3π/2,2π].

 

The cosine is decreasing in [0,π].

 

So both are true together for the set

 

[0,π] ∩ ( [0,π/2] ∪ [3π/2,2π] ) = ( [0,π] ∩ [0,π/2] ) ∪ ( [0,π] ∩ [3π/2,2π] )

 

= [0,π/2] ∪ ∅ = [0,π/2]