Mathematics 10 — Exercise 9.2 · Q8 (i)

Full question

Arc length 3 cm, radius 11/5 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. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{11\times 1}{1\times 5}$$

3. Calculate these two products separately.

   $$\frac{11}{5}$$

4. Calculate this operation before combining the remaining terms.

   $$11\times \frac{1}{5}=\frac{11}{5}$$

5. Substitute the given numbers into the formula.

   $$\frac{3}{\frac{11}{5}}$$

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

   $$\frac{1\times 5}{1\times 11}$$

7. Calculate these two products separately.

   $$\frac{5}{11}$$

8. Calculate this operation before combining the remaining terms.

   $$1\times \frac{5}{11}=\frac{5}{11}$$

9. Calculate this operation before combining the remaining terms.

   $$\frac{1}{\frac{11}{5}}=\frac{5}{11}$$

10. Calculate this operation before combining the remaining terms.

    $$3\times 5=15$$

11. Calculate this operation before combining the remaining terms.

    $$1\times 11=11$$

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

    $$\frac{15\times 1}{1\times 11}$$

13. Calculate this operation before combining the remaining terms.

    $$15\times \frac{1}{11}=\frac{15}{11}$$

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

    $$\frac{3\times 5}{1\times 11}$$

15. Calculate these two products separately.

    $$\frac{15}{11}$$

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

    $$\frac{5\times 1}{1\times 11}$$

17. Calculate this operation before combining the remaining terms.

    $$5\times \frac{1}{11}=\frac{5}{11}$$

18. Calculate this operation before combining the remaining terms.

    $$3\times \frac{5}{11}=\frac{15}{11}$$

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

    $$\frac{15}{11}$$

Answer

The final answer is shown below.