Normal and Tangent Lines - TRIG Practice

[Pages:3]Calculus

Name___________________________________ ID: 1

Normal and Tangent Lines - TRIG Practice

Date________________ Period____

For each problem, find the derivative of the function at the given value.

1) y = -2sin (x) at x = 3

4

2) y = cot (2x) at x = - 2

3

3) y = -csc (2x) at x = 5

6

4) y = -tan (x) at x = -

6

5) y = tan (2x) at x = 5

6

6) y = sec (2x) at x = -

2

-1-

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For each problem, find the equation of the line tangent to the function at the given point. Your answer should be in slope-intercept form.

( ) 7) y = -2cot (2x) at , 0 4

8) y = -2sin (x) at (, 0)

( ) 9) y = -csc (x) at - 2 , 2 3 33

10) y = sec (x) at (, -1)

For each problem, find the equation of the line normal to the function at the given point. If the normal line is a vertical line, indicate so. Otherwise, your answer should be in slope-intecept form.

( ) 11) y = sin (2x) at - , -1 4

( ) 12) y = -2cot (2x) at , - 2 3 63

( ) 13) y = 2csc (2x) at 5 , - 4 3 63

( ) 14) y = -tan (x) at - , 1 4

-2-

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Answers to Normal and Tangent Lines - TRIG Practice (ID: 1)

dy 1)

dx

= 2

x = 3 4

dy 2)

dx

=-8 3

x = - 2 3

dy 3)

= 4

dx

3

x = 5 6

dy 4)

dx

=-4 3

x=- 6

5) dy

= 8

dx

6) dy

= 0

dx

7) y = 4x -

8) y = 2x - 2

x = 5 6

x=- 2

9) y = - 2 x + 6 3 - 4

3

9

10) y = -1

11) Normal line is vertical line at x = - 4

12) y = - 3 x + -64 3 + 3

16

96

13) y = 3 x + -64 3 - 15

8

48

14) y = 1 x + 8 + 28

-3-

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