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Question

30 degree is equal to _________ radians.

The correct answer is

π/6

To convert an angle from degrees to radians, we use the fundamental relationship between the two units: a full circle is equivalent to 360 degrees, which is also equal to $2\pi$ radians.

Convert 30 Degrees to Radians

We know that:

  • $180^\circ = \pi \text{ radians}$

From this, we can find the conversion factor for 1 degree:

  • $1^\circ = \frac{\pi}{180} \text{ radians}$

To convert any angle from degrees to radians, we multiply the angle in degrees by the conversion factor $\frac{\pi}{180}$.

Calculation for 30 Degrees

Let's apply this to the given angle, which is 30 degrees:

  1. Start with the angle in degrees: $30^\circ$
  2. Multiply by the conversion factor: $30^\circ \times \frac{\pi}{180} \text{ radians}$
  3. Simplify the expression: $\frac{30 \times \pi}{180} \text{ radians}$
  4. Reduce the fraction. Both 30 and 180 are divisible by 30:
    • $30 \div 30 = 1$
    • $180 \div 30 = 6$
    So, the expression becomes: $\frac{1 \times \pi}{6} \text{ radians}$
  5. The result is: $\frac{\pi}{6} \text{ radians}$

Therefore, 30 degrees is equal to $\frac{\pi}{6}$ radians. This matches option 2.

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Important Questions from Angles and measures in degrees and radians

  1. If P = sin20 θ + cos48 θ, then the inequality that holds for all values of θ is

  2. Express \({\pi\over 12}\)  radians in degrees.

  3. Which of the following angles is same as 135° ?
  4. Which of the following is the best approximated degree measure of 4 radians?
  5. The radian equivalent of 150° is _______.
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