2 math 4r - files.transtutors.com · angles & their measure if each angle has the given measure...

2 Math 4RTrigonometry HOMEWORK

3

o o

-1 -1··

HW# 35:----

1_Finish WS (Packet Pg_ 1) - Angles & Their Measure2. WS (Packet Pg. 2) - Degree vs. Radian

HW#36:----

WS - Special Angles (Packet Pg 4) (Do not use a calculator)

HW#37:----

Text p. 414 - # 31, 33, 35, 36, 47, 48

HW# 38:----

1. WS (Packet Pg. 5) - Trigonometry Practice2. Study for Quiz!!! (NO CALCULATOR)

HW# 38A----

Solve each of the following:(1) 2x - 1 = 0 (2) 3x + -{3 = 0 (3) 4x - 1 = 2x + 1(4) S(x + 1) = S (5) 3(x - 2) = 2x - 7(6) x + ..J2 = 2..J2 (7) 2X2 - x - 1 = 0

HW# 39:----

WS (Packet Pg. 6) - Linear Trig Equations - # 1 - 9 ODD

HW#40:----

WS (Packet Pg. 7) - Quadratic Trig Equations

WS (Packet Pg. 9-10) - Trigonometry Review

HW # 41A: Study for Test!!!

Angles & Their Measure

If each angle has the given measure and is in standard position,determine the quadrant in which its terminal side lies.

1 7rr:12

2. _ 2rr:3

3. 371° 4. 14rr:5

5. -156° 6. 1000° 8. -240°

Change each degree measure to radian measure in terms of Te.

10. -250° 11. -145°

13. 870° 14. 18° 15. -820° 16. 345°

Change each radian measure to degree measure.

17. -1 18.4rr 19. -2.56 20. 12.85

21 3rr:16

22. _ 7rr:9

23. 13rr:30

24. _ 17rr:3

IFind the reference angle for each angle with the given measure.

25. -20° 26. 160° 27. -545° 28. 3000

29. 10rr:3

30. _ 5rr:8

31. -?:4

32. _ 7rr:6

Degree vs. Radians

Use a calculator to approximate each value to four decimal places.

2. sin710°

4.sin7

5. cotl1.55rr 6. csc34.78°

®

-1__ I _ . \ NAME DATE.r~- ----~ Practice Worksheet

, Trigonometric Functions of Special AnglesFind each exact value. Do not use a calculator.1 . rr 2 rr• sm 4" • cos 4" 3. tan :

4. cos 210° 5. sin 3000 6. tan 330°

311'7. sin ""4 3rr

8. cos ""4 3rr9. tan ""4

10. sin 90° 11. esc 270° 12. tan 45°

37T13. cos "2

37T14. tan "2

37T15. sin ""2

Use a calculator to approximate each value to four decimal places.16. cot (-75°) 17. sin 634° 18. cos 235°

19. sin 2 20. sec 4.28 21. cot 0.23

Special Angles

Find each exact value. Do NOT use a calculator.

1. cos60° 2 . 1f

.Sln-3

3. csc90°9rr:

4. tan-3

7rr:5. sec-3

6. cot4S0

7. sec270°5rr:

8. COs-6

9. 7rr:

.SLn-6

10. esc (_ 7;)

11. tan3rr 12. cot19

rr:3

Trigonometry Practice

1. Write 1600 in radian measure.

2. Write 5rr: in degrees.6

3. Evaluate and round to four decimal places.

(a) sin42° (b) sec(11.S0)

(d) cos e7

n)(c) tanS

(e) csc C~rr:)

4. Find the exact value without a calculator.

(a) tan60°rr:

(b) sinG

(c) cscn (d) sec!!..3

(e) cos420° (f) cot225°

(g) sin lln

6

(h) sec 3n

4

Linear Trig Equations

Find the exact solution set of each equation if 00 < (J < 360°.

1. 2cose - 1 = 0 2. 3tane + -J3 = 0

3. 4sine - 1= 2sine + 1 4. 5(cose + 1) = 5

5. 3(tane - 2) = 2tane - 7 6. sece + -/2 = 2-/2

Find the exact values for (J in the interval 0 < (J < Zn.

7. 3sine - -J3 = sine 8. scose + 3 = 3cose + 5

9. tane + 12 = 2tane + 11 10. sine + -/2 = {22

11. 3csce + 5 = csce + 9 12. 4(cote + 1) = 2(cote + 2)

Quadratic Trig Equations

Find the exact solution set of each equation if 00 < 6 < 360°.

1. tan28 - 3 = 0 2. 2sin28 + sin8 - 1 = 0

3. 2sin8cos8 + cos8 = 0

Find the exact values for 6 in the interval 0 < 6 < 2TC.

4. tan2e - 1 = 0 5. cos38 = cos8

6. 2sin8 - csc8 = 0

Sinusoidal Regression

Name: _

1) Raul is taking a Marine Biology course and is assigned to study the tides at the local beach. Raul took readings atfour-hour intervals to determine the behavior of the tides.

Depth (m) Time2.35 Midnight3.19 4a.m.1.81 8 a.m.2.41 Noon3.28 4 p.m.1.87 8 p.m.2.58 Midnight

(a) Use the data shown that Raul collected, where midnight is represented by' = 0, to model the tidal behavior

with a sinusoidal regression with all values rOlUldedto the nearest hundredth?

(b) Use the exact equation to predict the depth of the water at 6:00 a.m.

2)The amount of ice in the arctic changes throughout the year. Suppose the data below is for the

amount of ice (in millions of square miles) in the arctic for a period of one year.

Month (x) Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec.

Ice(y) 5.56 5.79 5.68 5.21 4.71 3.78 2.65 2.31 2.59 3.51 4.36 4.96

(a) If x = 1 represents January 1, fmd a sinusoidal function of

best fit for this data, rounding all values to the nearest

hundredth. A sinusoidal function has the form

y = a sin (bx + c) + d .

(b) Using the exact equation, determine the months in which there was the maximum

and minimum amount of ice in the arctic.

(c) According to the exact regression equation what will be the amount of ice during

March of the following year?

MATH4R NAME __

TRIGONOMETRY REVIEW DATE _

1. Find the reference angle for the angle measuring - 510° .

117Z'2. Find the reference angle for the angle measuring -- radians.

3

3 If I· d d . . 107Z' d' .. an ang e In stan ar position measures - -- ra lans, In which quadrant3

does its terminal side lie?

4. Change 7000 to radian measure in terms of 7Z' .

5. Change - ~ radians to degree measure.12

6. Simplify the expression:cosx - 2

cos2x - cosx - 2

. . . sec2x

7. Simplify the expression: 2

tan x

8. Find the exact value of each function without using a calculator.

. 12Jr ( Jr)(a) S1ll

4(b) cot600° (c)sec -3

9. Solve for x in the interval 0 S; x S; 2Jr

2cos2x + cosx - 1 = 0

10. Throughout the day, the depth of water at the end of a dock varies with the tides.The table shows the depths (in meters) at various times during the morning(Midnight is time 0 and Noon is time 12.)

t (time) Midnight 2 AM. 4AM. 6AM. 8 AM. 10 AM. Noony (depth) 2.55 3.80 4.40 3.80 2.55 1.80 2.27

(a) Use the regression capabilities of a graphing calculator to fit a trigonometricfunction in the form f1 (x)=a*sin(bx+c)+d to the data.(Round to the nearest hundredth.)

(b) Use the equation to predict the depths at 9 AM. and 3 P.M.