How to evaluate this Trig expression?

[ace799]

Directions

"If n is an integer, n * 180° represents an integer multiple of 180°, (2n + 1) * 90 represents an odd integer multiple of 90°, and so on. Decide whether each expression is equal to 0, 1, -1, or is undefined."

The question is:

cos[ (2n+1) * 90° ]

The answer in the back of the book is = 0 but I have no clue how its solved.
Any help would be great!

 

[Deleted member 4993]

Directions

"If n is an integer, n * 180° represents an integer multiple of 180°, (2n + 1) * 90 represents an odd integer multiple of 90°, and so on. Decide whether each expression is equal to 0, 1, -1, or is undefined."

The question is:

cos[ (2n+1) * 90° ]

The answer in the back of the book is = 0 but I have no clue how its solved.
Any help would be great!

cos(π/2) = 0

cos (π + Θ) = -cos(Θ)

cos(3π/2) = cos(π + π/2) = -cos(π/2) = 0

cos(5π/2) = cos(π + 3π/2) = -cos(3π/2) = 0

and so on....

 

[stapel]

Decide whether each expression is equal to 0, 1, -1, or is undefined."

The question is: cos[ (2n+1) * 90° ]

The answer in the back of the book is = 0 but I have no clue how its solved.

What did you try? What did you get when you started plugging in values for "n"? What patterns, if any, did you see?