# What is the equation of the line that is normal to #f(x)=-sinx +tanx # at # x=-pi/3#?

First, find the point the normal line will intercept:

To find the slope of the normal line, we must first find the slope of the tangent line. Since the normal line and tangent line are perpendicular, their slopes will be opposite reciprocals.

The derivative of the function is

The slope of the tangent line is

Graphed are the original function and its normal line:

graph{(y+sinx-tanx)(y+sqrt3/2+2/7(x+pi/3))=0 [-4.858, 2.94, -2.89, 1.007]}

By signing up, you agree to our Terms of Service and Privacy Policy

The equation of the line that is normal to f(x)=-sinx +tanx at x=-pi/3 is y = -√3x - 2√3.

By signing up, you agree to our Terms of Service and Privacy Policy

- What is the average rate of change of the function #g(t)=(t+2)^2# on the interval [t-h, t]?
- How do you find the derivative of #f(x)=4/sqrtx# using the limit process?
- How do you find the equation of the line tangent to the graph of #f(x)=sqrt( x-1)# at the point (5,2)?
- What is the equation of the tangent line of #f(x)=3x^2-x^3# at #x=1#?
- What is the equation of the line tangent to # f(x)=e^(x^2+x) # at # x=-1 #?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7