MCV 4UI – 2014/2015 Unit 11: Derivatives of Trig Functions

Date

/ Lesson /

Section

/

Assigned Work

/

Ö

. /
Derivatives of Sine and Cosine functions
/ 8.4 / Page 518 # 1 abcegh, 2 bcdefh, 3, 8
May 13
May 14 / Derivatives of other Trig Functions / 8.4 / Page 518 # 1df, 2ag
May 15
May 19 / Equations of Tangents, Max/Mins, P.O.I.’s / 8.4 / Page 518 #4, 5, 6, 9
May 20,
May 21 / Curve Sketching / Sketch


May 22
May 25 / Related Rates / 8.5 / Handout (attached to outline)
May 26
May 27 / QUEST
May 28
May 29 / Derivatives of / Handout
June 1
June 2 / Derivatives of
and
/ Handout
June 3
June4 / Logarithmic Differentiation / Handout
June
5,8,9 / / Exam Review
June 10 / / Exam Prep Day
Extra help
/ See web-site
Mon
Jun 22nd /
EXAM
/ 11:30 a.m. – 2:00 p.m.
See web-site for room

Answers to Related Rates Involving Trigonometry:

1.  lengthening at 25 m/h

2.  decreasing at 0.02 radians/second

3.  a) 11623.9 m/min b) 33708.44 m/min

4.  decreasing at 0.727 m2/s

5.  increasing at 0.283 m/s

6.  rotating at 0.128 radians/second.

Related Rates Involving Trigonometry

1.  The angle of elevation of the sun is decreasing at ¼ rad/h. How fast is the shadow cast by a building of height 50 m lengthening, when the angle of elevation of the sun is ?

2.  A kite 40 m above the ground moves horizontally at the rate of 3 m/s. At what rate is the angle between the string and the horizontal decreasing when 80 m of string has been let out?

3.  A revolving beacon is situated 925 m from a straight shore. It turns at 2 rev/min. How fast does the beam sweep along the shore at a point 1275 m from the nearest point?

4.  Two sides of a triangle are six and eight metres in length. If the angle between them decreases at the rate of 0.035 rad/s, find the rate at which the area is decreasing when the angle between the sides of fixed length is.

5.  A ladder 10 m long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 2 m/s, how fast is the angle between the top of the ladder and the wall changing when the angle is?

6.  A vehicle moves along a straight path with a speed of 4 m/s. A searchlight is located on the ground 20 m from the path and is kept focused on the vehicle. At what rate (in rad/s) is the searchlight rotating when the vehicle is 15 m from the point on the path closest to the searchlight?