Solving Trigonometric Equations, #2 (Grades 11-12)
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Solving Trigonometric Equations, #2
1.
Solve [math]cos(theta) + 2 = 1.4[/math] for [math]0 <= theta <=pi[/math]. Round the answer to 3 decimals places.
- 0.927
- 2.214
- -0.927
- 4.069
2.
Solve [math]sin(theta) + 0.3 = -0.3[/math] for [math] pi/2 <= theta <= (3pi)/2[/math]. Round the answer to 3 decimal places, if necessary.
- [math]pi[/math]
- 3.785
- 2.498
- 5.640
3.
Solve [math]tan(theta + (3pi)/4)+ 0.2 = 0.9[/math] on the interval [math]0 <= theta <= pi[/math]. Round the answer to 3 decimals places.
- 1.518
- 3.316
- 0.611
- 1.396
4.
Solve [math]sin(theta) -0.5 = 0.1[/math] on the interval [math]pi <= theta <= 2pi[/math]. Round the answer to 3 decimals places.
- No solution.
- 3.785
- 5.640
- 3.242
5.
Solve [math]cos(3/4 theta) = 5/8[/math] for [math]0 <= theta <= pi[/math]. Round the answer to 3 decimals places.
- 1.099
- 1.433
- 0.896
- 1.194
6.
Find the value(s) of [math]theta[/math] which satisfy the equation [math]cos(theta - 0.2) = 7/9[/math], given that [math]0 <= theta <= 2pi[/math]. There may be more than one correct answer. Round the answer(s) to 3 decimal places.
- 4.204
- 0.880
- 5.804
- 5.604
7.
Solve the equation [math]sin(x/2 + 4/3) + 0.3 = 0.75[/math] on the interval [math][0,2pi][/math]. There may be more than one correct answer. Round the answer(s) to 3 decimal places.
- 0.467
- 3.608
- 2.683
- 4.117
8.
Which of the following are correct solutions to the equation [math]tan(2(x-1/2)) = 4/5[/math] on the interval [math][0,2pi] ?[/math] Choose all correct answers. Round the answers to 3 decimal places.
- 0.675
- 0.837
- 2.408
- 5.550
9.
Solve [math]tan(1/4 x - 3) = 10[/math] on the interval [math][0,2pi][/math]. There may be more than one correct answer. Round the answer(s) to 3 decimal places.
- 1.471
- 2.177
- 5.318
- No solution.
10.
Which of the following are correct answers to the equation [math]sin(2theta-pi/2) + 1 = 1/2[/math] for [math]0 <= theta <= 2pi ?[/math] Choose all correct answers.
- [math]pi/6[/math]
- [math](5pi)/6[/math]
- [math](7pi)/6[/math]
- [math](5pi)/3[/math]
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