Answers and Explanations 267
Answers
401–500
To find the slope of the normal line, take the opposite reciprocal of the slope of the
tangent line to get − 1
19
.
Now use the point-slope formula for a line to get the normal line at (3, 28):
y
x
y
x
− = −
−
= −
+
28
1
19
3
1
19
535
19
(
)
406.
y
x
= − + π + 2
4
The normal line is perpendicular to the tangent line. You can begin by finding the
y value at x = π
4
, because it isn’t given:
( )
f π
π
4
4
2
2
1
2
2
2
( )






=
=
=
sin
Next, find the derivative of the function:
x
x
sin cos
= 2
( )
x
f '
Then substitute in the given x value to find the slope of the tangent line:
( )












π
π
π
4
2
4
4
2 2
2
2
2
1
=
=
=
sin cos
f '
To find the slope of the normal line, take the opposite reciprocal of the slope of the
tangent line to get –1.
Now use the point-slope formula for a line to get the normal line at x = π
4
:
y
x
y
x
− = −
−
= − + +
1
2
1
4
2
4
π
π
( )