Question

Sin(13pi/2) in periodic function

Answer 1

The value of sin(13pi/2) can be found by reducing the angle by multiples of 2pi radians, resulting in sin(pi/2), which is +1.

Step-by-step explanation:

The sine function is a periodic function that oscillates between +1 and -1. When looking at sin(13π/2), we need to understand that sine has a period of 2π radians. Therefore, we reduce the given angle 13π/2 by multiples of 2π until we find an equivalent angle that lies within one period of the sine function. In this case, 13π/2 can be simplified by subtracting 2π (2 units of π radians) repeatedly until we are left with an angle between 0 and 2π.

13π/2 is equivalent to 6.5π, and after subtracting 2π three times, we get π/2, which is the reduced angle within the range of one sine cycle. Hence the value of sin(13π/2) is the same as sin(π/2), which is +1.

Answer 2

answer: 1
13pi/2 can be simplified onto 6 pi/2, so it goes around the unit circle 6 times and left with pi/2. the coordinates of pi/2 is (0,1). the trigonometric function sin is y/r. since r is always 1 on the unit circle, the answer is the y value, in this case it is 1.