What is the angle between the graph of #f(x)=2sin(x)-1# and the #x#-axis if the graph of #f# intersects the #x#-axis at #x=pi/6#?

I worked out the tangent line to the graph of #f# at #(pi/6, 0)# and I got #y=2cos(x)*x-pi/6#

1 Answer
Aug 9, 2017

Answer:

The angle is #=pi/3#

Explanation:

We need

#(sinx)'=cosx#

#(a)'=0#

Our function is

#f(x)=2sinx-1#

The derivative with respect to #x# is

#f'(x)=(2sinx-1)'==(2sinx)'-(1)'=2cosx#

At the point #x=pi/6#,

#f'(pi/6)=2cos(pi/6)=2*sqrt3/2=sqrt3#

The slope of the tangent at #x=pi/6# is

#m=sqrt3#

The equation of the tangent is

#y=sqrt3(x-pi/6)#

#m=tanalpha=sqrt3#

Therefore,

The angle is #alpha=arctan(sqrt3)=60^@=pi/3#

graph{((2sinx-1))(y-(sqrt3)(x-pi/6))=0 [-0.915, 1.786, -0.586, 0.765]}