Convert the following in remaining two units of measurement of an angle: (i) 30º (ii) 2G (iii) R/3 π

Understand the Problem

The question is asking to convert angles given in degrees (30º), a variable notation (2G), and radians (π/3) into two other units of measurement for angles. This will typically involve converting degrees to radians and radians to degrees for the provided angles.

Answer

30º = $ \frac{\pi}{6} $, 2G = $ \frac{\pi}{90} $, $ \frac{\pi}{3} $ = 60º

Steps to Solve

Convert 30º to Radians

To convert degrees to radians, use the formula: $$ \text{radians} = \text{degrees} \times \frac{\pi}{180} $$

For 30º: $$ \text{radians} = 30 \times \frac{\pi}{180} = \frac{\pi}{6} $$

Convert 2G to Radians

The notation "2G" usually refers to "two times the angle of 1 degree." To convert this into radians: $$ 2G = 2 \times 1 \times \frac{\pi}{180} = \frac{2\pi}{180} = \frac{\pi}{90} $$

Convert π/3 to Degrees

To convert radians to degrees, use the formula: $$ \text{degrees} = \text{radians} \times \frac{180}{\pi} $$

For $$ \frac{\pi}{3} $$: $$ \text{degrees} = \frac{\pi}{3} \times \frac{180}{\pi} = 60 $$

Summary of Results

Now summarize the conversions:

30º = $$ \frac{\pi}{6} $$ radians
2G = $$ \frac{\pi}{90} $$ radians
$$ \frac{\pi}{3} $$ radians = 60º

30º = ( \frac{\pi}{6} ) radians, 2G = ( \frac{\pi}{90} ) radians, ( \frac{\pi}{3} ) radians = 60º

More Information

The conversion between degrees and radians is essential in trigonometry and helps relate circular measurements to linear measurements. Knowing these conversions allows you to work in either system based on your needs.

Tips

Forgetting to use the correct conversion factor (π/180 for degrees to radians, and 180/π for radians to degrees).
Mixing up the order of operations when converting.
Not recognizing the context of "2G" and treating it as a standard degree instead of a multiplication factor.

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