Question
How many radians is \( 777^{\circ} \) ? Give the exact answer in simplest form. \( \square \) radians
Ask by Gonzalez Watkins. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{259\pi}{60} \) radians
Solution
To convert 777° to radians, we use the conversion factor:
radians = (π/180) × degrees
So,
777° = (π/180) × 777 = (777π)/180
We simplify by dividing the numerator and denominator by 3:
777 ÷ 3 = 259
180 ÷ 3 = 60
Thus, the expression becomes:
= (259π)/60
This is the exact answer in simplest form.
Answer: (259π)/60 radians
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Simplify this solution Beyond the Answer
To convert degrees to radians, you can use the formula: \[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \] For \( 777^{\circ} \): \[ \text{radians} = 777 \times \frac{\pi}{180} = \frac{777\pi}{180} \] Next, simplify the fraction \( \frac{777}{180} \). The greatest common divisor (GCD) of 777 and 180 is 3: \[ \frac{777 \div 3}{180 \div 3} = \frac{259}{60} \] Thus, the exact answer in simplest form is: \[ \frac{259\pi}{60} \text{ radians} \]
