Pre-Calculus Assignment Sheet Unit 3: Basic Trigonometry September 24th – October 11th, 2013 Date Tuesday 9/24 Wednesday 9/25 Thursday 9/26 Friday 9/27 Monday 9/30 Tuesday 10/1 Wednesday 10/2 Thursday 10/3 Friday 10/4

Topic (4.1) Angles in Coordinate Plane – Degrees Notes pages 1 and 2 Paper Plate Activity for the Unit Circle

Assignment p.291 #31 – 46 all

30-60-90 and 45-45-90 right triangles place coordinates on the plate and go over HW from Monday

p. 299 #5 – 21 odd

(4.1) Angles in Coordinate Plane – Radians Notes page 3 (4.4) Reference Angles Notes page 4 QUIZ– Angles in Radians and Degrees (4.1) Arc Length and Sector Area Notes pages 4 & 5 (4.3) Right Triangle Trigonometry Notes bottom of page 5 (4.2) Unit Circle (day 3) discuss period and even/odd qualities of trig functions Notes top of page 6

p. 290 #7 – 23, 47 – 54 all, 55 – 69 odd

Monday 10/7

QUIZ- Arc Length, Sector Area, Reference Angles (4.3) Evaluate Trig Functions with a Calculator using Basic Trig Identities (introduce cofunctions p. 374) Notes bottom of page 6 (4.4) Trig Functions of any Value determine trig functions of any angles (in terms of x, y, and r), signs of trig values in quads +/- Notes p.7 QUIZ– Unit Circle (fill in the blanks) 4.4 more calculator trig , finding solutions to equations using unit circle Notes p.7 More Practice/ review pp.365 – 366 #3-87 odd – omit #s 21, 53, 55

p. 300 #43 – 52 p. 309 #27 – 35, 43 – 45

Tuesday 10/8 Wednesday 10/9 Thursday 10/10 Friday 10/11

Notes

Complete Paper Plate Unit Circle

NO SCHOOL

TEST #3 Basic Trigonometry (4.1 – 4.4) September 24th, 2013

p. 319 #37 – 44 (reference angles) p. 292 #79 – 94 , #95 – 100, 106, 107 p. 308 #1 – 4 all, 9 – 15 odd, 17 – 20 all p. 299 # 1, 3, 23 – 41 odd

p. 318 #1 – 7 odd, 11 – 14 all, 15 – 23 odd, 29 – 36 all, 45 – 64 all p. 319 #65 – 86

Study for test tomorrow!!! Print Unit 4

(4.1) Angles in Coordinate Plane – Degrees

Vocab: angle in standard position initial side terminal side vertex positive angles negative angles coterminal angles rotation Draw and label degrees of circle on the axis of the coordinate plane.

1

State the Quadrant in which the terminal side of the given angle lies and draw the angle in standard position. 1. 187°

2. – 14.3°

3. 245°

4. – 120°

5. 800°

6. 1075°

7. – 460.5°

8. 315°

9. – 912°

10.

11. 537°

12. – 345.14°

13°

Find two angles, one positive and one negative angle, that are coterminal with the given angle. 13. 74°

14. – 81°

15. 115.3°

16. 275°

Find the complement and supplement for the given angles.

17. – 180°

19. 17.11°

18. – 310°

20. 45.2°

Find the degree measure of the angle for each rotation. Draw the angle in standard position. 21.

5 rotation, clockwise 8

22.

3 rotation, counterclockwise 5

23.

7 rotation, counterclockwise 9

24.

17 rotation, clockwise 4

25.

3 rotation, clockwise 10

26.

5 rotation, counterclockwise 6

2

September 30th, 2013

Notes

(4.1) Angles in Coordinate Plane – Radians

Determine the quadrant in which each angle lies and sketch the angle in standard position. 1.

 7

2.

 9

3.

6 5

4.

 5 7

5.

17 8

6.

3.7 r

7.

 4.2 r

Find the complement and supplement of each angle, if possible. 8.

 7

9.

6 5

10.

3r

11.

Find the Radian Measure of the angle with the given Degree Measure 12. 330  13. –72  14. 145 

15. 765 

Find the Degree Measure of the angle with the given Radian Measure. 18.



7 2

19.

5 6

20.

1.5 r

2 9

21.

 12

16. 36 

22. 2

r

17. –120 

23. -1.5

r

III. Find two co-terminal angles for the following. One Positive and One Negative. 24. 135 

25.

11 6

26.





27. -50 

4

IV. Determine if the following are co-terminal. 28. -30  , 330 

29.

5 17 , 6 6

30.

32 11 , 3 3

31. 50  , 340 

3

October 1st, 2013

Notes:

Reference Angles

Definition of a reference angle:

Find the reference angle 1.

  32

6.



11.

 7

1.4 r

'

and sketch

2.

  132

7.



12.



9 7

2.8 r

 ' in standard position. 3.

  132

8.



13..

October 2nd, 2013

Notes:

and

 4 5

4.22 r

4.

  232

9.



14.

 2 7

5.95 r

5.

  200

20 9

10.



15.

 1.7 r

Arc Length and Area of a Sector

Arc length

Area of a Sector

Find the length of the arc on a circle of radius, r, with central angle,  . 1.

r  4; 

 6

2.

r  3.5; 

3 4

3.

r  10;  60

Find the radian measure of the central angle of a circle with radius, r, that intercepts an arc length, s. 4. r = 20, s = 15

5. r= 33 inches, s = 6 inches

Find the area of a sector with radius, r, and central angle,

.

4

1.

r  5;  120

2.

r  8.4; 

2 3

Applications 1. Pittsburg, PA is located at 40.5  N while Miami is located at 25.5  N. Assuming the Earth is a perfect sphere, how many miles apart are the two cities (Earth radius is 4,000 miles).

2. A sprinkler can spray water 75 feet and rotates through an angle of 135  . Find the area of the region that the sprinkler covers.

October 3rd, 2013

Notes:

hypotenuse

Right Triangle Trigonometry

side opposite

 side adjacent to

sin  

csc 

cos  

sec 

tan 

cot  





Find the exact value of the six trigonometric functions of the angle  shown in the figure.

2. Sketch a right triangle corresponding to the trig function, determine the third side and then find the 5 remaining trig functions.

csc  3 10

 24

5

October 4th, 2013

Notes:

Even, odd qualities of Trig Functions

Given the coordinate, determine the exact value of the six trig functions.

1.

  5 12  ,    13 13 

2.

 15  8   ,   17 17 

5.

sin

Evaluate the trig function using its period and your plate. 3. cos 7

4.

EVEN Trig. functions: ODD Trig functions:

6. If

sin

11 4

cos( x)  cos x sin( x)   sin x tan( x)   tan x

csc t  5 then csc( t )  _______

and

6.

cos

 15 6

sec( x)  sec x csc( x)   csc x cot( x)   cot x

sin t  ______ then sin(t )  _______

October 7th, 2013

Notes:

 7 2

Cofunctions, Calculator Trig.

Cofunction Identities:

  sin  u   cos u 2 

  cos  u   sin u 2 

  tan  u   cot u 2 

  csc  u   sec u 2 

  sec  u   csc u 2 

Remember

 2

  cot   u   tan u 2 

 90

Use a calculator to evaluate the trig. function, Round to 4 decimal places. 1.

sin

 5

5. cos 38

3 7

2.

csc

6.

cot 77.5

3.

tan1.28

7. sin 57.8

4.

sec .77

8.

csc 29.5

Use the given function values to find the indicated trig values. Draw a triangle or use your plate. 9.

10.

cos 30 

1 2

tan   3

tan 30  _____

sec 30  _______

cos(90  30) 

cot   _____

sin   ______

sin90     _______ 6

October 8th, 2013

Notes:

Trig Functions of any angle

Definition of Trig Functions of any angle: Let a point on the terminal side of

sin  



and

 be an angle in standard position with ( x, y)

r  x 2  y 2  0 . Then: cos  

csc 

1. Determine the exact value of the 6 trig functions given

State the quadrant(s) in which

sec 

cot  

tan  =

(4,  7) . Draw a triangle.

 lies.

2.

tan  0

3.

sin  0 tan  0

4.

cos  0

5.

sin  0 cos  0

6.

sin   cos

7.

sin   0 cos   0

Find the values of the 6 trig functions with the given restraints. Draw a triangle. 8.

cos  

Find

10.

3 5

9. csc  2

 lies in Quadrant IV

 , for 0     , for the following problems.

sin  

3 2



=_____

11.

October 9th, 2013

Notes: 1.

cos 125

5.

sec

3 5

cos   0

Put answer in radians.

cos  1



= ______

12.

tan  undefined



= ________

More Calculator Trig and Solving Trig Equations

2.

csc168

3.

cot 150

4.

sin 345

6.

cos

 2 7

7.

tan

13 8

8.

sin 3.42 r

Find two solutions for the given equations. Use your paper plate.

9.

cos  

3 2

10.

sin  

 3 2

11.

csc   2

12.

cot   3

7