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
Answer for screen readers
30º = ( \frac{\pi}{6} ) radians, 2G = ( \frac{\pi}{90} ) radians, ( \frac{\pi}{3} ) radians = 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.