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Trigonometry Review (Grades 11-12)

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Trigonometry Review

1. 
In [math]DeltaABC[/math], [math]angA[/math] is a right angle and [math]mangB=30deg[/math]. If [math]AB = 30 \ "ft"[/math], find [math]AC[/math].
  1. [math]20sqrt3[/math] ft
  2. [math]10sqrt3[/math] ft
  3. [math]60[/math] ft
  4. [math]3sqrt2[/math] ft
2. 
If side [math]AB = 15[/math] and [math]ang C = 38 deg[/math] What is the length of [math]AC[/math]?
Right Triangle ABC v2
  1. 24.4
  2. 19.2
  3. 9.2
  4. 19.0
3. 
If side [math]AC = 17[/math] and [math]ang C = 12 deg[/math], what is the length of [math]BC[/math] ?
Right Triangle ABC v2
  1. 16.6
  2. 3.6
  3. 17.4
  4. 3.5
4. 
If side [math]AB = 15[/math] and [math]ang C = 38 deg[/math], what is the length of [math]BC[/math] ?
Right Triangle ABC v2
  1. 24.4
  2. 19.2
  3. 9.2
  4. 19.0
5. 
If [math]sin(theta)=7/25[/math], what is [math]tan(theta)[/math]?
  1. [math]7/24[/math]
  2. [math]24/25[/math]
  3. [math]7/8[/math]
  4. [math]24/7[/math]
6. 
If [math]tantheta= 5/12[/math], what is [math]sin theta[/math]?
  1. [math]12/13[/math]
  2. [math]5/13[/math]
  3. [math]13/5[/math]
  4. [math]12/5[/math]
7. 
Given [math]sin(theta)=7[/math] and [math]cos(theta)=1[/math]. Find [math]tan(theta)[/math] using the appropriate quotient identity.



8. 
The                           is defined as half the difference between the maximum and minimum values of a periodic function.
  1. period
  2. amplitude
  3. phase shift
  4. resonance
  5. none of these are correct
9. 
Secant is the reciprocal of                .
  1. sine
  2. cosine
  3. tangent
  4. cosecant
10. 
The reciprocal of [math]sintheta[/math] is                          .
  1. [math]1/(costheta)[/math]
  2. [math]1/(sectheta)[/math]
  3. [math]1/(cottheta)[/math]
  4. [math]1/(tantheta)[/math]
  5. none of these are correct
11. 
If [math]costheta = 20/29[/math], then what is [math]csctheta[/math]?
  1. [math]29/20[/math]
  2. [math]21/29[/math]
  3. [math]29/21[/math]
  4. [math]20/21[/math]
12. 
If [math]sin(theta)=24/25[/math] what is [math]csc(theta)? [/math]
  1. [math]25/24[/math]
  2. [math]7/24[/math]
  3. [math]24/3[/math]
  4. [math]25/7[/math]
13. 
Tangent of [math]30deg[/math] is equal to [math](sin 30deg)/(cot30deg)[/math].
  1. True
  2. False
14. 
Simplify. [math] (csc x tan x - cosx ) \ cotx[/math]
  1. [math]sin x[/math]
  2. [math]cos x[/math]
  3. [math]1[/math]
  4. [math]tan x[/math]
15. 
Determine the reference angle for an angle that is in standard position and the terminal side intersects the point [math](-6,2)[/math] (round to one decimal place).
  1. [math]123.7deg[/math]
  2. [math]56.3deg[/math]
  3. [math]47.8deg[/math]
  4. [math]18.4deg[/math]
  5. none of these are correct
16. 
Given that [math] 0deg < a < 360deg[/math], then the equation [math] cos(a) = -1[/math] has:
  1. one solution
  2. no solutions
  3. two solutions
  4. three solutions
  5. four solutions
17. 
If [math] 0deg < a < 360deg [/math], then the equation [math] sin(a) = cos(a) [/math] has:
  1. no solutions
  2. two solutions
  3. three solutions
  4. one solution
  5. four solutions
18. 
Which of the following is not equivalent to [math]cos(pi/5)[/math]?
  1. [math]cos((-pi)/5)[/math]
  2. [math]cos((9pi)/5)[/math]
  3. [math]cos((4pi)/5)[/math]
  4. [math]cos((11pi)/5)[/math]
19. 
Evaluate the following:
a) [math]sin((3pi)/4)[/math]


b) [math]cos((7pi)/3)[/math]



20. 
Which of the following is equal to Cos(186)?
  1. Cos(6)
  2. Cos(94)
  3. Cos(174)
  4. -Cos(94)
21. 
Which of the following is equal to Sin(721)?
  1. Sin(359)
  2. Sin(181)
  3. Sin(89)
  4. Sin(179)
22. 
Evaluate. [math]cot (pi/2)[/math]
  1. [math]sqrt2/2[/math]
  2. [math]1[/math]
  3. [math]0[/math]
  4. none of the above
23. 
Find [math]sec(495)[/math].
  1. [math]-sqrt(2) / 2 [/math]
  2. [math]1[/math]
  3. [math]− sqrt2 [/math]
  4. [math]-1[/math]
24. 
If [math]AB=17[/math], [math]ang C = 26deg[/math], and [math]AC= 6[/math], what is value of [math]ang B[/math] ?
Scalene Triangle ABC v1
  1. [math]3.2 deg[/math]
  2. [math].4 deg[/math]
  3. [math]1.2 deg[/math]
  4. [math]8.9 deg[/math]
25. 
Given [math]Delta ABC[/math], where [math]a=4, b=15, c=13[/math], find [math]m ang B[/math].
Scalene Triangle ABC v3
  1. 112.62°
  2. 53.15°
  3. 14.25°
  4. 97.87°

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