Question

Find the points at which the curve
y=sin x has horizontal tangents

Answer 1

Answer:

Step-by-step explanation:

Points on the curve y=sinx that have tangent lines through the origin satisfy:

slope of curve at (x,y) is  

x

y

​

=  

x

sinx

​

.

By simple differentiation, the slope of the curve at x is cosx, so our points satisfy

cosx=  

x

sinx

​

 

∴x=tanx or tan  

−1

x=x

So we have

y=sinx=sin(tan  

−1

x)=  

x  

2

+1

​

 

x

​

 

∴y  

2

=  

x  

2

+1

x  

2

 

​

 

y  

2

(x  

2

+1)=x  

2

⇒x  

2

y  

2

=x  

2

−y  

2