Home > Calculus > Tangent Line to a Curve

How do you find the equation of tangent line to the curve #y = sin(x)# at x = pi?

Answer 1

Charles Anctil

#x+y=pi#.

At x = #pi, y = sin pi =0#.

y'=cos x. So, at #x = pi, y'=cos pi=-1#.

Now, the equation of the tangent at #x=pi# is

#y-0=-1(x-pi)#

Answer: #x+y=pi#.

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

Answer 2

Emily Ammerman

To find the equation of the tangent line to the curve y = sin(x) at x = pi, we need to find the slope of the tangent line and a point on the line.

The slope of the tangent line can be found by taking the derivative of the function y = sin(x) with respect to x. The derivative of sin(x) is cos(x).

At x = pi, the value of cos(pi) is -1. Therefore, the slope of the tangent line is -1.

To find a point on the line, we substitute x = pi into the original equation y = sin(x). At x = pi, sin(pi) is 0. Therefore, the point on the line is (pi, 0).

Using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values we found to get the equation of the tangent line.

Substituting m = -1 and the point (pi, 0), the equation of the tangent line is y = -x + pi.

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

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.