Question

What values for theta(0 <= theta <= 2pi) satisfy the equation?
2 sin theta cos theta + sqrt 3 cos theta = 0

a. pi/2, 4pi/3, 3pi/2, 5pi/3
b. pi/2, 3pi/4, 3pi/2, 5pi/3
c. pi/2, 3pi/4, 3pi/2, 5pi/4
d. pi/2, pi/4, 3pi/2, 5pi/3

Answer 1

2 sin t cos t + √3 cos t = 0
cos t ( 2 sin t + √3 ) = 0
Therefore:
cos t = 0,   t 1 = π/2,  t 2 = 3 π/2
or:
2 sin t + √3 = 0
2 sin t = - √3
sin t = - √3 / 2
t 3 = 4 π/3,  t 4 = 5 π/3
Answer:
a ) π/2, 4π/3, 3π/2. 5π/3.

Answer 2

HI!!! I just finished the unit 7 lesson 11 unit test!! Here are the answers: :)

1. A: 2

2. C: 225

3. C: pi/4

4. A: -465

5. C: 0

6. B: 210

7. B: 2pi

8. A: 52

9. C: 40

10. C: 3rd graph

11. A: y=sin pi/265

12. B: 1/4pi

13. D: y=3cos2

14. A: sqrt3/3

15. C: 0

16. C: 3rd graph

17. A: 187

18. C: sqrt2/2

19. B: 1+sin theta

20. D: 45

21. D: 0.64

22. A:80

23. C: pi/2, 5pi/4, 3pi/2, 7pi/4

24. C: csc theta =13/12, sec theta= 13/5

hope this helps someone :)))