Question

convert into degree ... 5/6 radian​

Answer 1

Answer- The above question is from the chapter 'Trigonometric Functions'.

Concept used: To convert radian into degrees, multiply by $\frac{180^{\circ}}{\pi}$ .

Similarly, to convert degrees into radians, multiply by $\frac{\pi}{180^{\circ}}$ .

Example: Let us take 2π/3 radians.

$\frac{2 \pi}{3} \times \frac{180^{\circ}}{\pi}\\\\= \frac{2 \times 180^{\circ}}{3}\\\\= 2 \times 60^{\circ}\\= 120^{\circ}$

Now, 120° in radians is as follows.

$120^{\circ}\\= 120^{\circ} \times \frac{\pi}{180^{\circ}}\\\\= \frac{2 \pi}{3} \: radians$

Given question: Convert 5π/6 radians into degrees.

Solution: Following is the conversion.

$\frac{5 \times \pi}{6}\\\\= \frac{5 \times \pi}{6} \times \frac{180^{\circ}}{\pi} \\\\= \frac{5 \times 180^{\circ}}{6}\\\\= 5 \times 30^{\circ}\\= 150^{\circ}$