Questions: Convert the angle in degrees to radians. -210° -210°= radian(s) (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression)

$Convert the angle in degrees to radians. -210° -210°= radian(s) (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression)$

Transcript text: Convert the angle in degrees to radians. \[ \begin{array}{r} -210^{\circ} \\ -210^{\circ}= \end{array} \] $\square$ radian(s) (Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression

Solution

Solution Steps

To convert an angle from degrees to radians, use the formula: radians = degrees × (π/180). This formula is derived from the fact that 180 degrees is equivalent to π radians. Apply this formula to the given angle of -210 degrees.

Step 1: Understand the Conversion Formula

To convert an angle from degrees to radians, use the formula: \[ \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) \]

Step 2: Apply the Formula

Given the angle $-210^\circ$, substitute it into the formula: \[ \text{radians} = -210 \times \left(\frac{\pi}{180}\right) \]

Step 3: Simplify the Expression

Calculate the multiplication: \[ \text{radians} = -210 \times \left(\frac{\pi}{180}\right) = -\frac{210\pi}{180} = -\frac{21\pi}{18} = -\frac{7\pi}{6} \]