Evaluate sin(101pi)

Answer 1

101π = 50(2π) + π

sin 101π = sin π

Answer 2

Sin values range from -1 to 1 for any value. Looking at the sin graph any whole number multiplied by Pi, like 0pi, 1pi, 2pi, 10pi, etc. is equal to 0. Knowing this you can evaluate Sin(101pi) to be 0. Since 101pi is a whole number multiplied by pi it will equal zero.

If you want to visualize it I recommend using a graphing calculator or a free graphing website like Desmos and plugging in the equations y = sin(x) and x = 101pi

Finding the intersection point of these two lines will show that at the x value of 101pi the y value will be equal to 0