Calculus
posted by George .
Consider the function f(x)=sin(1/x)
Find a sequence of xvalues that approach 0 such that
sin (1/x)=0
sin (1/x)=1
sin (1/x)=1
Is sin sin (1/x)=0 and sin (1/x)=1 does not exist.
What is sin (1/x)=1 then.

Calculus 
drwls
sin (1/x) = 0 if 1/x = pi, which means x = 1/pi
sin (1/x) = 1 if 1/x = pi/2, which means x = 2/pi
sin (1/x ) = 1 if 1/x = 3 pi/2, which means x = 2/(3 pi)
I don't understand why the x values should approach zero, or what the rules of the sequence are.
Respond to this Question
Similar Questions

tigonometry
expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by b and using that cos(b)= cos(b) sin(b)= sin(b) gives: sin(ab) = sin(a)cos(b)  cos(a)sin(b) … 
algebra
Can someone please help me do this problem? 
math
Eliminate the parameter (What does that mean? 
Mathematics  Trigonometric Identities
Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y … 
Calculus
Consider the function f(x)=sin(1/x) Find a sequence of xvalues that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=1 Is sin sin (1/x)=0 and sin (1/x)=1 does not exist. What is sin (1/x)=1 then. How would I show the sequence … 
Calculus
Consider the function f(x)=sin(1/x) Find a sequence of xvalues that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if … 
Calculus
Consider the function f(x)=sin(1/x) Find a sequence of xvalues that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if … 
TRIG!
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1  (3/4)sin^2 2x work on one side only! Responses Trig please help!  Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 … 
Calculus
Hello, Could somebody kindly check my answer for the following question? 
Trigonometry
Solve the equation for solutions in the interval 0<=theta<2pi Problem 1. 3cot^24csc=1 My attempt: 3(cos^2/sin^2)4/sin=1 3(cos^2/sin^2)  4sin/sin^2 = 1 3cos^2 4sin =sin^2 3cos^2(1cos^2) =4sin 4cos^2 1 =4sin Cos^2  sin=1/4 …