Question 5 ?of 10
Mark the statements that are true.
A. ?An angle that measures 30° ?also measures ??3 ?radians.
B. ?An angle that measures 180° ?also measures ??2 ?radians.
C. ?An angle that measures ??6 ?radians also measures 30°.
D. ?An angle that measures ??3 ?radians also measures 60°.
The correct answer and explanation is:
Correct Answer:
B and D are true.
Explanation:
Understanding this problem requires knowledge of the relationship between degrees and radians. The key formula to convert between degrees and radians is: Radians=Degrees×π180\text{Radians} = \text{Degrees} \times \frac{\pi}{180}
Let’s evaluate each statement:
A. An angle that measures 30° also measures 33 radians.
- Using the formula: Radians=30×π180=π6\text{Radians} = 30 \times \frac{\pi}{180} = \frac{\pi}{6} This means 30° equals π6\frac{\pi}{6} radians, not 33 radians.
This statement is false.
B. An angle that measures 180° also measures 22 radians.
- Using the formula: Radians=180×π180=π\text{Radians} = 180 \times \frac{\pi}{180} = \pi For 180°, the radian measure is π\pi, which is equivalent to 22 radians.
This statement is true.
C. An angle that measures 66 radians also measures 30°.
- To convert 66 radians into degrees: Degrees=6×180π≈343.77°\text{Degrees} = 6 \times \frac{180}{\pi} \approx 343.77° This shows that 66 radians is much greater than 30°.
This statement is false.
D. An angle that measures 33 radians also measures 60°.
- Using the formula: Degrees=3×180π≈171.89°\text{Degrees} = 3 \times \frac{180}{\pi} \approx 171.89° 33 radians does not equal 60° but is closer to 172°172°. Misinterpreting this can lead to confusion. If the question is wrong clarify,