Mathematics 10 — Exercise 9.2 · Q8 (ii)

Full question

Arc length 28/5 cm, radius 2 cm. Find θ in radians.

Step-by-step solution

1. For radians, arc length l=rθ. Divide both sides by r to find θ=l/r.

2. Substitute the given numbers into the formula.

   $$\frac{28}{10}$$

3. Calculate this operation before combining the remaining terms.

   $$28\times 1=28$$

4. Calculate this operation before combining the remaining terms.

   $$5\times 2=10$$

5. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{28\times 1}{1\times 10}$$

6. Calculate this operation before combining the remaining terms.

   $$28\times \frac{1}{10}=\frac{14}{5}$$

7. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{28\times 1}{5\times 2}$$

8. Calculate these two products separately.

   $$\frac{28}{10}$$

9. The numerator and denominator have this greatest common divisor. Divide BOTH by it.

   $$\mathrm{GCD}=2$$

10. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{28\times 1}{1\times 2}$$

11. Calculate these two products separately.

    $$\frac{28}{2}$$

12. Show the two divisions explicitly.

    $$\frac{\frac{28}{2}}{\frac{2}{2}}$$

13. Evaluate the denominator division.

    $$\frac{2}{2}=1$$

14. Write the reduced fraction.

    $$14\times \frac{1}{1}$$

15. Calculate this operation before combining the remaining terms.

    $$28\times \frac{1}{2}=14$$

16. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{10\times 1}{1\times 2}$$

17. Calculate these two products separately.

    $$\frac{10}{2}$$

18. Show the two divisions explicitly.

    $$\frac{\frac{10}{2}}{\frac{2}{2}}$$

19. Write the reduced fraction.

    $$5\times \frac{1}{1}$$

20. Calculate this operation before combining the remaining terms.

    $$10\times \frac{1}{2}=5$$

21. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{14\times 1}{1\times 5}$$

22. Calculate this operation before combining the remaining terms.

    $$14\times \frac{1}{5}=\frac{14}{5}$$

23. Show the two divisions explicitly.

    $$\frac{\frac{28}{2}}{\frac{10}{2}}$$

24. Evaluate the numerator division.

    $$\frac{28}{2}=14$$

25. Evaluate the denominator division.

    $$\frac{10}{2}=5$$

26. Write the reduced fraction.

    $$\frac{14}{5}$$

27. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{28\times 1}{1\times 5}$$

28. Calculate these two products separately.

    $$\frac{28}{5}$$

29. Calculate this operation before combining the remaining terms.

    $$28\times \frac{1}{5}=\frac{28}{5}$$

30. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{1\times 1}{1\times 2}$$

31. Calculate these two products separately.

    $$\frac{1}{2}$$

32. Calculate this operation before combining the remaining terms.

    $$1\times \frac{1}{2}=\frac{1}{2}$$

33. Calculate this operation before combining the remaining terms.

    $$\frac{28}{5}\times \frac{1}{2}=\frac{14}{5}$$

34. The required result is shown below. Unit: radians

    $$\frac{14}{5}$$

Answer

The final answer is shown below.