Question

Please help me with this. Numbers 1-11

Answer 1

Answer:

1. 8.378

2. 3.534

3. 12.566

4. 0.262 rad or $\frac{\pi }{12}$

5. 1.222 rad or $\frac{7\pi }{18}$

6.  5.236 rad or $\frac{5\pi }{3}$

7. 240°

8. 165°

9. 22.5°

10. 30° = $\frac{\pi }{6}$ radians

45° = $\frac{\pi }{4}$ radians

$\frac{\pi }{3}$ radians = 60°

$\frac{\pi }{2}$ radians = 90°

120° = $\frac{2\pi }{3}$ radians

$\frac{3\pi }{4}$ radians = 45°

$\pi$ radians = 180°

$\frac{3\pi }{2}$ radians = 270°

360° = $2\pi$ radians

11. 9.424 inches

Step-by-step explanation:

Problems 1-3:

S=r*Ф

S= arc length, r= radius, Ф= angle in radians

You need to convert the angle from degrees to radians before you can use it in the equation. You do this by multiplying it by pi and dividing by 180. Then you can plug this and the radius into the equation to solve for the arc length.

1) 120° x $\frac{\pi }{180}$ = 2.094 rad

S= 4 x 2.094 = 8.378

2) 135° x $\frac{\pi }{180}$ = 2.356 rad

S= 1.5 x 2.356 = 3.534

3) 240° x $\frac{\pi }{180}$ = 4.189 rad

S= 3 x 4.189 = 12.566

Problems 4-6:

4) 15° x $\frac{\pi }{180}$ = 0.262 rad or $\frac{\pi }{12}$

5) 70° x $\frac{\pi }{180}$ = 1.222 rad or $\frac{7\pi }{18}$

6) 300° x $\frac{\pi }{180}$ = 5.236 rad or $\frac{5\pi }{3}$

Problems 7-9:

7) $\frac{4\pi }{3} *\frac{180}{\pi } =$ 240°

8) $\frac{11\pi }{12} *\frac{180}{\pi } =$ 165°

9) $\frac{\pi }{8} *\frac{180}{\pi } =$ 22.5°

Problem 10:

30° = $\frac{\pi }{6}$ radians

45° = $\frac{\pi }{4}$ radians

$\frac{\pi }{3}$ radians = 60°

$\frac{\pi }{2}$ radians = 90°

120° = $\frac{2\pi }{3}$ radians

$\frac{3\pi }{4}$ radians = 45°

$\pi$ radians = 180°

$\frac{3\pi }{2}$ radians = 270°

360° = $2\pi$ radians

Problem 11:

S= r * Ф

S= 4 * $\frac{3\pi }{4}$

S= 3$\pi$ = 9.424 inches

Answer 2

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