Question

Determined the quadrant for an angle with the following characteristics: cotθ>0 and cscθ>0.

Answer 1

$\csc\theta=\dfrac1{\sin\theta}>0\implies\sin\theta>0$

This happens whenever the terminal point of $\theta$ lies in either the first or second quadrants.

Meanwhile,

$\cot\theta=\dfrac1{\tan\theta}=\dfrac{\cos\theta}{\sin\theta}>0\implies\cos\theta>0$

since you already know sine is positive. Cosine is positive when the angle lies in the first or fourth quadrant.

Sine and cosine are both positive only when $\theta$ is the first quadrant, which means this angle's terminal point lies in the first quadrant (A).

Answer 2

Answer:

1. B (tanX=x/y)

2. B (cscZ=x/z)

3. C (12/13)

4. B. (68.90)

5. B (39.81)

6. C (44)

7. B (2.9 cm)

8. B (523.8 ft)

9. A (pi radians)

10. D (5pi/6 radians)

11. B (70)

12. A (100.27)

13. B (3pi/4)

14. A (3pi/4)

15. C (sqrt3/2)

16. C (sqrt2/2)

17. D (tan pi/2)

18. D (sqrt 2/2)

19. B (cos52)

20.A (Quadrant I)

21. B (pi/3)

22. D (tan0=3sqrt7/3)

23. Written

Step-by-step explanation: