Find the x-intercepts of the graph

Question

y=sin nx/10 +1

Answer 1

Hi Austin.

 

To find the x-intercepts, one must set y=0

 

0 = sin(nx/10) + 1

 

Now solve this for "x"

 

Add (-1) to both sides to isolate the sine term

 

-1 = sin(nx/10)

 

 

The only angle whose sine is (-1) is -90º  (if you are working in degrees)  or -(pi/2)  if you are working in radians.

 

If there is no limit on the domain of this function, there are an infinite number of correct answers.

 

The angles whose sine is (-1) could also be 270°, or 630°, or 990°, or ...

 

Likewise, if you are in radians, other angles whose sine is (-1) are -5(pi)/2, -(9pi)/2,  3(pi)/2, 7(pi)/2, or ....

 

So if sin(nx/10) = -1, and only the sin(-90) = -1, then nx/10 = -90.

 

Solving for x, x=-900/n

 

If you were working in radians,  then nx/10 = -(pi/2)

 

Solving for x,  x = -10(pi)/2n  which simplifies to  x =  -5(pi)/n

 

If you want the infinite other solutions, just set nx/10 = 270,  nx/10 = 630, ...

 

Or in radians, set  nx/10 = 3(pi)/2,  nx/10 = 7(pi)/2, ....