Download Practice B - TeacherWeb

Name———————————————————————— Lesson
9.3
Date —————————————
Practice B
For use with the lesson “Evaluate Trigonometric Functions of Any Angle”
Use the given point on the terminal side of an angle u in standard position
to evaluate the six trigonometric functions of u.
1. (8, 215)
2. (27, 22)
Evaluate the six trigonometric functions of u.
3. u 5 908
4. u 5 2π
Sketch the angle. Then find its reference angle.
6. 1258
y
7. 3258
x
y
y
x
7π 9. 2​ }   ​
4
x
17π 8. 2​ } 
  
​
6
y
11π 10.​ }
  
​ 
3
y
x
y
x
x
Evaluate the function without using a calculator.
11. sin 2408
2
3π 15. cos​1 2}
​  4   ​  ​
12. tan 1508
13. sec(23158)
14. cot(21508)
7π 16. csc }
​     ​
6
8π 17. tan }
​     ​
3
5π 18. sin​1 2}
​  6   ​  ​
Lesson 9.3
19. Distance A projectile is launched with an initial speed of 42 feet per second. It is
9-28
projected at an angle of 508. How far does the projectile travel? How much farther
does it travel if it is launched with an initial speed of 84 feet per second?
20. Baseball A baseball player hits a ball projected at an angle of 408. The height at
which the ball is hit is the same as the height of the fence. At what speed must the
baseball player hit the ball in order for it to clear a fence that is 385 feet away?
Algebra 2
Chapter Resource Book
2
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
5. 21158
}
Teaching Guide
1. about 366.9 ft 2. about 407.5 ft
3. your friend; about 40.6 ft
Investigating Algebra Activity
y
y
x
r
1. sin u 5 ​ } ​, cos u 5 }
​ r ​, tan u 5 }​ x ​, csc u 5 }​ y ​,
r
}
​Ï3 ​ 
x
r
1
​ 2 ​, cos u 5​ }
   ​,
sec u 5 }​ x ​, cot u 5 }​ y ​ 2. sin u 5 }
2
}
}
}
​Ï3 ​ 
2​Ï 3 ​ 
​  3   
 ​, cot u 5 Ï
​ 3 ​ 
tan 5 }
​  3   ​, csc u 5 2, sec u 5 }
3. A; Answers will vary.
Practice Level A
3
5
4
4
1. sin u 5 }
​ 5 ​, cos u 5 }
​ 5 ​, tan u 5 }
​ 3 ​, csc u 5 }
​ 4 ​,
}
5
3
2​Ï13 ​ 
​ 3 ​, cot u 5 }
​ 4 ​ 2. sin u 5 }
​  13   
​, 
sec u 5 }
}
}
3​Ï 13 ​ 
2
​Ï13 ​ 
  
 tan u 5 2​ } ​, csc u 5 }
,
​
​ 
  
 ​,
cos u 5 2​ }
13
3
2
}
​Ï13 ​ 
3
  
​,  cot u 5 2​ }2 ​ 3. sin u 5 1,
sec u 5 2​ }
3
Practice Level B
15
15
8
1. sin u 5 2​ } ​,  cos u 5 }
​ 17  ​,  tan u 5 2​ }
  ​,
17
8
17
8
17
 ​,  sec u 5 }
​ 8  ​, cot u 5 2​ }
  ​
csc u 5 2​ }
15
15
}
}
2​Ï53 ​ 
7​Ï 53 ​ 
2. sin u 5 2​ }
  
​, cos u 5 2​ }
  
​, 
53
53
}
}
​Ï53 ​ 
​Ï53 ​ 
2
​ 7 ​, csc u 5 2​ }
  
​,  sec u 5 2​ }
  
​, 
tan u 5 }
7
2
7
​ 2 ​ 3. sin u 5 1, cos u 5 0, tan u is
cot u 5 }
undefined, csc u 5 1, sec u is undefined, cot u 5 0
4. sin u 5 0, cos u 5 21, tan u 5 0, csc u is
undefined, sec u 5 21, cot u is undefined
5.
y
6.
u 5 1258
x
u9 5 658
x
u 5 21158
658 558
y
7.
8.
u 5 3258
17p
6
p
u95 358
x
358 ​ }
  ​
6
y
10.
y
u 5 113p
p
u9 5 4
7p
u524
y
x
u9 5 6
π 9.
608 608
y
7.
8.
y
u52
x
u 5 2408
x
y
u9 5 558
cos u 5 0, tan u is undefined, csc u 5 1,
sec u is undefined, cot u 5 0 4. sin u 5 0,
cos u 5 21, tan u 5 0, csc u is undefined,
sec u 5 21, cot u is undefined
y
y
5.
6.
}
}
x
u9 5 p3
x
u 5 34p
x
x
π y
10.
y
}
19. about 54.3 ft, about 163 ft
u 5 76p
20. about 112 ft/sec
x
x
u
π π ​ }
  ​ ​ }  ​
6
3
A54
π }
508 ​ }
  ​
4
9.
π ​ }
  ​ ​ }  ​
4
3
}
}
Ï
​Ï 3 ​ 
​ 3 ​ 
11. 2​ }   ​ 12. 2​ }   ​ 13. ​Ï 2 ​  14. Ï
​
3 ​ 
2
3
}
}
​Ï 2 ​ 
1
15. 2​ }   ​ 16. 22 17. 2​Ï 3 ​  18. 2​ } ​
2
2
u 5 21308
Algebra 2
Chapter Resource Book
5 253p
Practice Level C
}
}
5​Ï74 ​ 
7​Ï 74 ​ 
5
}
}
1. sin u 5 2​     
​, cos u 5 2​  74   
​, tan u 5 }
​ 7 ​,
74
}
}
​Ï74 ​ 
​Ï 74 ​ 
7
}
}
​,  sec u 5 2​  7   
​,  cot u 5 }
​ 5 ​
csc u 5 2​  5   
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
answers
Lesson 9.3 Evaluate
Trigonometric Functions of
Any Angle
u 5 1208
}
​Ï3 ​ 
1
Ï
​Ï 3 ​ 
​ 3 ​ 
​Ï 2 ​ 
11. ​ }   ​ 12. }
​  3   ​ 13. }
​  2   ​ 14. 2​ }
   ​ 15. 2​ } ​
3
2
2
1
16. 2 17. 22 18. 2​ } ​ 19. 32 ft 20. no
2