Unit 12 trigonometry homework 1 answer key pythagorean theorem

13 Pythagorean Theorem and its Converse

Answers

1. 194

2. 63

3. 53

4. c = 10

5. 4 10

6. 65

7. Yes

8. No

9. No

10. Yes

11.

12.

1. 1122 ( )( ) baab a abb ++→( 22 ++ 2 )

2. 22 ⎛⎞⎜⎟⎝⎠ 111222 ab c + 22 →( ab c +)

3. Students must provide proof.

13 Sine, Cosine and Tangent

Answers

10.

2. 23.

3. 0.

4. 1

5. 0.

6. 0.

1. sin NNN === 343554 , cos , tan ; sin MMM === 434553 , cos , tan

2. xy ≈≈5, 6.

3. xy ≈≈11, 4.

4. xy ≈≈8, 10

5. bc ≈≈17, 12.

6. ca ≈≈23, 6.

7. ab ≈≈15, 16.

8. 17

9. 12

13 Application Problems

Answers

1. 11 in

2. 477 m

3. 35 m

4. 97 ft

5. 39 °

6. 88 ft

7. 31 °

8. 97 ft

9. 29 ft

10. 13 miles

11. The hypotenuse is always the longest side. Therefore, the ratios, HO < 1 and HA < 1.

13 Introduction to Angles of Rotations, Coterminal Angles and Reference Angles

Answers

1. − 458 °, 262 °

2. 115 °, − 245 °

3. − 570 °, 150 °

4. − 313 °, 407 °

5. − 302 °, 58 °

6. −6,  714° °

7. 353 , 367°− °

8. QII, 78 °

9. QIV, 40 °

10. QIII, 47 °

11. QIII, 80 °

12. QIV, 56 °

13. QIII, 71 °

14. QIV, 12 °

15. All the angles between 0 °and 90 ° are acute angles between the terminal side of the angle and the x-axis.

13 Trigonometric Ratios on the Unit Circle

13 Reciprocal Trigonometric Functions

13 Trigonometric Ratios of Points on the Terminal

Side of an Angle

Answers

1. (34,298°)

2. (52,45°)

3. (13,4)

4. (41,1)

5. (45,2)

6. (10,127°),

sin127 434553 ,cos127 ,tan127 ,csc127 ,sec127 ,cot °= 553434 °=− °=− °= °=− °=−

7. (15,270°),

sin 270 1,cos270 0,tan 270°=− °= °= und ,csc270 1,sec270°− °= und ,cot270 0°=

8. (241,321°),

sin 321 441 ,cos321 541 , tan 321 4 ,csc321 41 ,sec321 41 , cot 321°=− 541 °= 41 °=− 5 °=− 4 °= 5 °=− 4

9. (8,30°),

sin30 133 ,cos30 ,tan30 ,csc30 2,sec30 23 ,cot30 3 °=22 3°= °= °= °= 3 °=

10. (6 2,135°),

sin135 22 ,cos135 ,tan135 1,csc135 2,sec135 2,cot135 1 °= 22 °=− °=− °= °=− °=−

11. ( )9,π , sin 0,cosππ ππ π π==−1,tan 0,csc== = und ,sec −1,cot = und

1. ⎛⎞⎜⎟⎝⎠13 2, 74 π ,

sin72727 7,cos ,tan 11,csc 2,sec7 72,cot 1 42 42 4 4 4 4

ππππππ=− = =− =− = =−

1. ( 13,0),

sin 0 313 ,cos0 213 , tan 0 ,csc0 313 ,sec0 13 ,cot 0 2 ====== 13 13 2 3 2 3

1. ⎛⎞⎜⎟⎝⎠14, 43 π ,

sin43414 4234 43,cos ,tan 3,csc ,sec 2,cot 32 323 3 3 3 33

ππππ ππ=− =− = =− =− =

1. (45,2),

sin 2 5251 ,cos 2 , tan 2 ,csc2 5,sec2 2 5,cot 2 2 =− 552 =− = =− =− =

13 Law of Sines with AAS and ASA

Answers

1. mA a b ∠= °56 , 8, 10≈ ≈

2. mC a b ∠= °30 , 9, 6≈ ≈

3. mA c a ∠= °65 , 5, 13≈ ≈

4. mA a c ∠= °106 , 73, 59≈ ≈

5. mB c b ∠= °83 , 37, 41≈ ≈

6. mC b a ∠= °33 , 16, 15≈ ≈

7. mB c b ∠= °55 , 7, 9≈ ≈

8. mA b c ∠= °95 , 24, 11≈ ≈

9. mC a c ∠= °102 , 7, 11≈ ≈

10. mC a b ∠= °25 , 87, 53≈ ≈

11. 79 feet

12. 123 meters

13 The Ambiguous Case – SSA

Answers

1. 2 triangles

2. 2 triangles

3. 1 triangle

4. No triangle

5. 2 triangles

6. one triangle, mB ∠≈39°, mC ∠≈75°and c ≈10.

7. two triangles, mB ∠≈ 61 °, mC ∠≈ 78 °and c ≈13 or mB ∠≈ 119 °, mC ∠≈ 20 ° and c ≈4.

8. two triangles, mB ∠≈59°, mC ∠≈87°and c ≈ 22 or mB ∠≈120°, mC ∠≈26°and c ≈9.

9. one triangle, mB ∠≈ 41 °, mA ∠≈ 87 °and a ≈ 76

10. no triangle

11. two triangles, mB ∠≈78°, mC ∠≈67°and c ≈33 or mB ∠≈101°, mC ∠≈44°and c ≈24.

13 Law of Cosines with SAS (to find the third side)

3. 24.

6. 30.

10. 31.

• 1. Answers
• 1. −
• 1. −
• 1. −
• 1. −
• 1. −
• 1. 1. Undefined
• 1. 1. Answers
• 1. -0.
• 1. -1.
• 1. -0.
• 1. -1.
• 1. -1.
• 1. -1.
• 1. -1.
• 1. −
• 1. − 14. Undefined
• 1. −
• 1. 1. Answers
• 1. 1. 1. If cos90 0°= , then cab ab 222 =+−2 (0), or cab 222 =+.

13 Law of Cosines with SSS (to find an angle)

Answers

1. 38 °

2. 138 °

3. 65 °

4. 56 °

5. 50 °

6. 123 °

7. 47 °

8. 88 °

9. 119 °

10. 26 °

11. 88 °

12. 49 °