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Trigonometry Questions - All Grades

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Grade 11 Trigonometry CCSS: HSF-TF.A.3
In triangle ABC, [math]sin(C) = 1/2[/math]. If [math]AC = 6 \ "units"[/math], what is the length of [math]bar{BC} ?[/math]
Right Triangle ABC v2
  1. [math]2 \ "units"[/math]
  2. [math]2sqrt(3) \ "units"[/math]
  3. [math]12 \ "units"[/math]
  4. [math]4sqrt(3) \ "units"[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the exact value of [math]cos(285°) ?[/math]
  1. [math]1/2 (1 - sqrt(2))[/math]
  2. [math]-1/4 (sqrt(6) - sqrt(2))[/math]
  3. [math]1/4 (sqrt(6)-sqrt(2))[/math]
  4. [math]1/4 (sqrt(2) + sqrt(6))[/math]
Grade 11 Trigonometry CCSS: HSG-SRT.D.10
Which of the following is true concerning the law of sines and right triangles?
  1. The law of sines is not valid for right triangles.
  2. The law of sines can only be proved for the acute angles of a right triangle.
  3. The law of sines can be easily proved for a right triangle, using trig ratios and the fact that [math]sin(90°)=1[/math].
  4. The law of sines can proved for a right triangle, and the easiest proof involves the use of the Pythagorean Theorem and the formula for the area of a triangle.
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the exact value of [math]sin(105°) ?[/math]
  1. [math]1/2(sqrt(3)+sqrt(2))[/math]
  2. [math]1/4(sqrt(2)-sqrt(6))[/math]
  3. [math]1/4(sqrt(6)+sqrt(2))[/math]
  4. [math]1/4(sqrt(6)-sqrt(2))[/math]
Grade 11 Trigonometry CCSS: HSG-SRT.D.10
In [math]Delta LMN[/math], [math]LM = 7.5 \ "units"[/math], [math]MN = 6 \ "units"[/math], and [math]m ang L = 49°[/math]. Using the law of sines and the given information, which of the following is true?
  1. No such triangle exists.
  2. These measurements result in a unique triangle.
  3. These measurements result in two possible triangles.
  4. The law of sines cannot be used in this situation.
Grade 11 Trigonometry CCSS: HSF-TF.A.2
[math](-4pi)/3[/math] is equivalent to which of the following?
  1. [math](-2pi)/6[/math]
  2. [math](4pi)/3[/math]
  3. [math]pi/3[/math]
  4. [math](2pi)/3[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the exact value of [math]tan(165°) ?[/math]
  1. [math]2-sqrt(3)[/math]
  2. [math]-2-sqrt(3)[/math]
  3. [math]2+sqrt(3)[/math]
  4. [math]-2+sqrt(3)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the exact value of [math]sin(345°) ?[/math]
  1. [math]1/2(sqrt(2)-1)[/math]
  2. [math]-1/4 (sqrt(2)+sqrt(6))[/math]
  3. [math]1/4(sqrt(6) - sqrt(2))[/math]
  4. [math]1/4(sqrt(2) - sqrt(6))[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the exact value of [math]tan(255°) ?[/math]
  1. [math]-2-sqrt(3)[/math]
  2. [math]-2+sqrt(3)[/math]
  3. [math]2-sqrt(3)[/math]
  4. [math]2+sqrt(3)[/math]
Grade 11 Trigonometry CCSS: HSG-SRT.D.10
In [math]Delta XYZ[/math], [math]XY = 12 \ "units"[/math], [math]YZ = 15 \ "units"[/math], and [math]m ang X = 50°[/math]. Using the law of sines and the given information, which of the following is true?
  1. No such triangle exists.
  2. These measurements result in a unique triangle.
  3. These measurements result in two possible triangles.
  4. The law of sines cannot be used in this situation.
Grade 11 Trigonometry CCSS: HSG-SRT.D.10
In [math]Delta FGH[/math], [math]FG = 3 \ "units"[/math], [math]GH = 2 \ "units"[/math], and [math]m ang F = 30°[/math]. Using the law of sines and the given information, which of the following is true?
  1. No such triangle exists.
  2. These measurements result in a unique triangle.
  3. These measurements result in a two possible triangles.
  4. The law of sines cannot be used in this situation.
Grade 11 Trigonometry CCSS: HSG-SRT.D.10

This question is a part of a group with common instructions. View group »

What is the missing reason in step 16?
  1. Algebra (addition)
  2. Quadratic Formula
  3. Substitution Property of Equality
  4. Distributive Property
Grade 11 Trigonometry CCSS: HSF-TF.C.8
If [math]tan(theta) = sqrt(11)/11[/math] and [math]pi < theta < (3pi)/2[/math], what is the value of [math]sec(theta) ?[/math]
  1. [math]-(2sqrt(33))/11[/math]
  2. [math]sqrt(110)/11[/math]
  3. [math](2sqrt(33))/11[/math]
  4. [math]-sqrt(110)/11[/math]
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