Question

What's the value of sin{nπ+(-1)ⁿ π/6}? ​

Answer 1

Answer:

0 if n is an even integer and +1 or -1 if it’s odd. In fact it’s 1 if n can be written as 2k+1 (if k is an integer, so 1, 5, 9 etc) and -1 if n can be written as 2k-1 (3, 7, 11 etc)

This is because the sine graph reaches a maximum of 1 at PI/2 (90 degrees) and again at 360+90 and 720+90 etc and it reaches its minimum of -1 at -90, 360–90 etc (or in radians -pi/2, 3pi/2 etc) and it reaches 0 when n=O, 2, 4 etc (pi, 2pi etc).