Solving Trigonometric Equations (Grades 11-12)

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Solving Trigonometric Equations

1. 
For [math]-pi/2 <= theta <= pi/2[/math], solve [math]sin(theta) = sqrt(2)/2 [/math].
  1. [math]-pi/4[/math]
  2. [math]pi/4[/math]
  3. [math](3pi)/4[/math]
  4. [math]pi/3[/math]
2. 
Solve [math]cos(theta) = sqrt(3)/2[/math] on the interval [math][0, pi][/math].
  1. [math](2pi)/3[/math]
  2. [math](5pi)/6[/math]
  3. [math]pi/3[/math]
  4. [math]pi/6[/math]
3. 
Solve [math]tan(theta) = 1[/math] on the interval [math](-pi/2, pi/2)[/math].
  1. [math]pi/3[/math]
  2. [math]pi/2[/math]
  3. [math]pi/4[/math]
  4. [math]-pi/4[/math]
4. 
Solve [math]sin(theta) = 4/9[/math] on the interval [math](-pi/2, pi/2)[/math]. Round the answer to 3 decimal places.
  1. 2.681
  2. -0.461
  3. 0.461
  4. 0.589
5. 
Solve [math]tan(theta) = 1/8[/math] for [math]-pi/2 < theta < pi/2[/math]. Round the answer to 3 decimal places.
  1. -1.450
  2. 1.450
  3. 0.719
  4. 0.124
6. 
Solve [math]sin(theta) = 1/2[/math] for [math]0 <= theta <= 2 pi[/math]. Choose all correct answers.
  1. [math]pi/6[/math]
  2. [math]pi/3[/math]
  3. [math](5pi)/6[/math]
  4. [math]-pi/6[/math]
7. 
Solve [math]tan(theta) = 0.46[/math] for [math]0 <= theta <= 2pi[/math]. Choose all correct answers, rounded to 3 decimal places.
  1. 0.431
  2. 1.140
  3. 3.573
  4. 5.852
8. 
Solve [math]cos(theta) = -3/10[/math] on the interval [math][0, 2pi][/math]. Choose all correct answers, rounded to 3 decimal places.
  1. -1.266
  2. 1.266
  3. 1.875
  4. 4.408
9. 
Solve [math]sin(theta) = -3/4[/math] on the interval [math][-pi/2, (3pi)/2][/math]. Choose all correct answers, rounded to 3 decimal places.
  1. -0.848
  2. 2.293
  3. 3.990
  4. 5.435
10. 
Solve [math]cos(theta) = 9/10[/math] on the interval [math][-pi, pi][/math]. Choose all correct answers, rounded to 3 decimal places.
  1. -2.691
  2. -0.451
  3. 0.451
  4. 2.691

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