Question

what's the value of sin{nπ+(-1)ⁿ π/6} , When n is a integer​

Answer 1

Answer:

The proof depends on the value of n

Consider  sin (nπ +(−1)nπ/6)  

Now, when the value of n is odd i.e.. n=1,3,5,7……..

Then the argument of the function is (nπ-π/6),

This argument lies in the second quadrant and by the knowledge of trigonometry sin(x) is positive in the second quadrant.

And nπ-π/6 is a multiple of π/6

So sin(nπ-π/6) = 1/2.

Now , when n is even

The argument of the function is nπ+π/6 which lies in the first quadrant again sin(x) is positive in the first quadrant .

And nπ+π/6 is a multiple of π/6

So sin(nπ+π/6) = 1/2.

Step-by-step explanation: