Reading Strategy

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LESSON Reading Strategy

11-5 Analyze Information

You can use double-angle identities and half-angle identities to evaluate expressions and find exact values. One step is to find the sign of the functions of the angle.

Use the diagram above to determine the sign of each function of in each quadrant. Write + or - next to the function name.

Quadrant I Quadrant II Quadrant III Quadrant IV

1.

sin

sin

sin

sin

2.

cos

cos

cos

cos

3.

tan

tan

tan

tan

Determine the quadrant and sign of each trigonometric expression.

4. sin330?

5. cos210?

6. sin150?

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7. tan123?

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8. sin290?

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9. cos13?

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10. sin194?

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11. cos359?

12. tan275?

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13. cos178?

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14. tan205?

15. sin85?

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Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

11 - 4 2

Holt McDougal Algebra 2

Reading Strategy

Quadrant Quadrant Quadrant Quadrant

I

II

III

IV

1. sin +

sin +

sin -

sin -

2. cos +

cos -

cos -

cos +

3. tan +

tan -

tan +

tan -

4. QIV, - 6. QII, + 8. QIV, - 10. QIII, - 12. QIV, - 14. QIII, +

5. QIII, - 7. QII, - 9. QI, + 11. QIV, + 13. QII, - 15. QI, +

11-6 SOLVING TRIGONOMETRIC EQUATIONS

Practice A 1. a. 2 sin = - 3

b. sin = - 3 2

c. 240? + 360?n, 300? + 360?n 2. 120? + 360?n, 240? + 360?n 3. 45? + 180?n 4. a. cos2 - 2cos + 1 = 0

b. (cos - 1)2 = 0 c. 0?, 360? 5. 71.6?, 108.4?, 251.6?, 288.4? 6. 0?, 48.6?, 131.4?, 180?, 360? 7. a. 1 - sin2 = sin2 + sin

b. sin = -1, sin = 1 2

c. 30?, 150?, 270? 8. 0?, 30?, 150?, 180?, 360? 9. 45?, 135?, 225?, 315? 10. 26?, 64?

Practice B 1. 120? + 180?n 2. 45? + 360?n, 135? + 360?n 3. 120? + 360?n, 240? + 360?n

4. 30? + 180?n

5. 45?, 225?

6. 45?, 135?, 225?, 315?

7. 90?

8. 7 6

9. 45?

10. 232.7?, 317.6?

11. 0?, 120?, 180?, 240?, 360?

12. 45?, 135?, 225?, 315?

13. 45?, 135?, 225?, 315?

14. 36.4?, 57.5?

15. 3:47 A.M., 7:13 A.M., 3:47 P.M., 7:13 P.M.

Practice C

1. 150? + 180?n

2. 120? + 360?n, 240? + 360?n

3. 60?, 120?, 240?, 300?

4. 51.8?

5. 7 , 5 64

6. 45?, 90?, 135?, 225?, 270?, 315?

7. 60?, 180?, 300? 9. 141.3?, 218.7?

8. 30?, 90?, 150? 10. ; 7

44

11. 0?, 60?, 180?, 300?, 360?

12. 0?, 90?, 360?

13. 0?, 270?, 360?

14. March 24 and October 4

Reteach

1. tan = 3 or - 3 ;

3

3

30?, 150?, 210?, 330? 2. 2x2 - x = 0

x(2x - 1) = 0 x = 0 or 2x - 1 = 0

x = 0 or x = 1 2

sin = 0 or sin = 1 2

0?, 30?, 150?, 180?

3. x2 - 2x + 1; (x - 1)2; cos = 1; 0?

4. 2x2 - 7x + 3 = 0

(2x - 1)(x - 3) = 0

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

A55

Holt McDougal Algebra 2

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