Applying the Pythagorean Identity (Grades 11-12)

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Applying the Pythagorean Identity

1. 
Which of the following is an alternate form of the Pythagorean Identity? Choose all correct answers.
  1. [math]tan^2(theta) + sin^2(theta) = 1[/math]
  2. [math]tan^2(theta) + 1 = sec^2(theta)[/math]
  3. [math]1 + sec^2(theta) = cot^2(theta)[/math]
  4. [math]1 + cot^2(theta) = csc^2(theta)[/math]
2. 
Given that [math]cos(theta) = 3/7[/math] and [math]0 < theta < pi/2[/math], what is the value of [math]sin(theta)?[/math]
  1. [math](2sqrt(10))/7[/math]
  2. [math]40/49[/math]
  3. [math]sqrt(58)/7[/math]
  4. [math]58/49[/math]
3. 
Given that [math]sin(theta) = -0.56[/math], find the value of [math]cos(theta)[/math], given than [math]pi < theta < (3pi)/2[/math]. Round the answer to 3 decimal places.
  1. -0.828
  2. 0.828
  3. 0.686
  4. -0.686
4. 
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]
5. 
If [math]csc(theta) = -(7sqrt(3))/3[/math] and [math](3pi)/2 < theta < 2pi[/math], what is the value of [math]cot(theta) ?[/math]
  1. [math]-sqrt(138)/3[/math]
  2. [math]sqrt(138)/3[/math]
  3. [math](2sqrt(39))/3[/math]
  4. [math]-(2sqrt(39))/3[/math]
6. 
If [math]tan(theta) = -4/9[/math] and [math]pi/2 < theta < pi[/math], what is the value of [math]sin(theta) ?[/math]
  1. [math](4sqrt(97))/97[/math]
  2. [math]sqrt(97)/4[/math]
  3. [math](9sqrt(97))/97[/math]
  4. [math](9sqrt(65))/65[/math]
7. 
If [math]sin(theta) = -0.446[/math] and [math](3pi)/2 < theta < 2pi[/math], what is the value of [math]tan(theta) ?[/math] Round the answer to 3 decimal places.
  1. -1.899
  2. -0.407
  3. -0.498
  4. 0.498
8. 
If [math]sin(theta) = sqrt(5)/4[/math] and [math]pi/2 < theta < pi[/math], what is the value of [math]sec(theta) ?[/math]
  1. [math]-sqrt(11)/4[/math]
  2. [math]-(4sqrt(21))/21[/math]
  3. [math]sqrt(11)/4[/math]
  4. [math]-(4sqrt(11))/11[/math]
9. 
What is the value of [math]cos(theta)[/math] if [math]cot(theta) = 1/9[/math] and [math]pi < theta < (3pi)/2 ?[/math]
  1. [math]-sqrt(82)/82[/math]
  2. [math]-sqrt(10)/10[/math]
  3. [math]-sqrt(5)/20[/math]
  4. [math]-sqrt(2)/4[/math]
10. 
What is the value of [math]tan(theta)[/math] if [math]sin(theta) = -3/8[/math] and [math](3pi)/2 < theta < 2pi ?[/math]
  1. [math]-sqrt(55)/3[/math]
  2. [math]-(3sqrt(55))/55[/math]
  3. [math]-sqrt(73)/3[/math]
  4. [math]-(3sqrt(73))/73[/math]

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