If tan0=-3/4 and 0 is in quadrant iv, cos20= (33/25, -17/25, 32/25, 7/25, 24/25? ) and tan20= (24/7, -24/7, 7/25, -7/25, 13/7, -13/7? ) . more information in the picture

Step-by-step explanation:

Sometimes, it is easiest to let a calculator do the work. (See below)

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The magnitude of the tangent is less than 1, so the reference angle will be less than 45°. Then double the angle will be less than 90°, so will remain in the 4th quadrant, where the cosine is positive and the tangent is negative.

You can also use the identities ...

  cos(2θ) = (1 -tan(θ)²)/(1 +tan(θ)²)

  cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)

  cos(2θ) = 7/25

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  tan(2θ) = 2tan(θ)/(1 -tan(θ)²) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)

  tan(2θ) = -24/7

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

5   1/4   miles per hour

step-by-step explanation:

15   3/4 / 3 = 5   1/4