All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
3601
Convert 3π/4 radians to degrees.
Answer:
135°
Multiply the given radian measure by 180°/π. So, (3π/4) * (180°/π) = 3 * (180°/4) = 3 * 45° = 135°.
3602
Convert 120° into circular measure (radians).
Answer:
2π/3
To convert 120° to radians, multiply by π/180. 120 * (π/180) = 120π / 180. Dividing the numerator and denominator by 60 leaves 2π/3 radians.
3603
What is the fundamental formula relating arc length (l), radius (r), and central angle (θ) in radians?
Answer:
l = rθ
The fundamental definition of radian measure states that the angle θ in radians is the ratio of the arc length l to the radius r (θ = l/r). Rearranging this formula yields l = rθ.
3604
Convert 45° into radians.
Answer:
π/4
Using the conversion formula (Degrees * π/180), we calculate 45 * (π / 180). This fraction simplifies to 1/4, giving π/4 radians.
3605
Convert π/6 radians to degrees.
Answer:
30°
To convert radians to degrees, multiply the radian measure by 180°/π. Thus, (π/6) * (180°/π) = 180° / 6 = 30°.
3606
What is the radian measure of 60°?
Answer:
π/3
The conversion factor from degrees to radians is π/180. Multiplying 60 by π/180 gives 60π/180, which simplifies exactly to π/3 radians.
3607
Convert 90° into radians.
Answer:
π/2
To convert degrees to radians, multiply the angle in degrees by π/180°. Therefore, 90° * (π / 180°) = 90π / 180 = π/2 radians.
3608
How many degrees are there in exactly one radian?
Answer:
Approx 57.3°
One radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius. Since π radians = 180°, 1 radian = 180°/π. Using π ≈ 3.14159, 1 radian is approximately equal to 57.2958°, or roughly 57.3°.
3609
What is the measure of one complete revolution in radians?
Answer:
2π
One complete revolution represents a full circle, which equals 360 degrees. In circular measure, 360 degrees is exactly equal to 2π radians. Therefore, one full revolution corresponds to 2π radians.
3610
Find the equation of a line passing through the origin that is parallel to the line y = 5x + 2.
Answer:
y = 5x
Step 1: Parallel lines share the exact same slope. The given line y = 5x + 2 has a slope of 5. Step 2: The new line must also have a slope of 5, making its equation y = 5x + c. Step 3: Because it passes through the origin (0,0), its y-intercept c is 0. The equation is y = 5x.