The function is .
(Apply derivative)
(The trigonometric of
)
To find the slope at ,
Evaluate (Slope of the graph at
)
(Simplify)
Then, using the point-slope form of the equation is:
\ (Point-slope form)
(Substitute
)
(Apply distributive property: a(b + c) = ab + ac)
(Simplify)
(Add 2 to each side)
Therefore the equation of the tangent lint at is
.
Use a graphing utility to graph the function and its tangent line at the point:
\