Problem 2.
Convert the angle
𝜃
=
−
1
2
from radians to degrees.
(A)
−
90
∘
(B)
90
∘
(C)
−
(
90
𝜋
)
∘
(D)
(
90
𝜋
)
∘
(E)
−
(
180
𝜋
)
∘

Question

Problem 2.
Convert the angle 
𝜃
=
−
1
2
 from radians to degrees.
(A) 
−
90
∘
(B) 
90
∘
(C) 
−
(
90
𝜋
)
∘
(D) 
(
90
𝜋
)
∘
(E) 
−
(
180
𝜋
)
∘

BlackTom AI · Accepted Answer

π radians equals 180°, so convert radians to degrees by multiplying by 180/π.

Relevant knowledge points:
- A radian is defined so that π radians = 180°. 
- The conversion factor from radians to degrees is 180/π: degrees = radians × (180/π).

Step-by-step reasoning and intermediate steps:
1. Interpret the given angle as θ = −π/2 radians (this matches the form that converts to −90°).
2. Apply the conversion: degrees = (−π/2) × (180/π).
3. Cancel the π factors: (−π/2) × (180/π) = −(1/2) × 180.
4. Compute the multiplication: −(1/2) × 180 = −90.

Thus θ = −90°.

Why the correct answer is correct:
Multiplying −π/2 by 180/π directly uses the fundamental equivalence π = 180°, so the π’s cancel and you are left with −180/2 = −90. That is exactly option A.

Why the other options are incorrect:
- B (90°) has the wrong sign; +90° corresponds to +π/2, not −π/2.
- C (−(90/π)°) and D ((90/π)°) show degrees expressed with a π in the denominator; those are not degrees but a misapplied factor (they would numerically be ≈ −28.65° and 28.65° respectively if interpreted numerically), so they do not equal −90°.
- E (−(180/π)°) equals approximately −57.2958°, which corresponds to −1 radian, not −π/2 radians.

Conclusion: The correct converted angle is −90°, which matches answer A.

Problem 2. Convert the angle 𝜃 = − 1 2 from radians to degrees. (A) − 90 ∘ (B) 90 ∘ (C) − ( 90 𝜋 ) ∘ (D) ( 90 𝜋 ) ∘ (E) − ( 180 𝜋 ) ∘单项选择题

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