Questions: 135° = radians

Transcript text: \[ 135^{\circ}= \] $\square$ radians

Solution

Solution Steps

To convert degrees to radians, use the formula: radians = degrees × (π / 180). Apply this formula to convert 135 degrees to radians.

Step 1: Convert Degrees to Radians

To convert an angle from degrees to radians, use the formula: \[ \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) \] Substitute $135^\circ$ into the formula: \[ \text{radians} = 135 \times \left(\frac{\pi}{180}\right) \]

Step 2: Simplify the Expression

Calculate the multiplication: \[ \text{radians} = 135 \times \left(\frac{\pi}{180}\right) = \frac{135\pi}{180} \] Simplify the fraction: \[ \frac{135}{180} = \frac{3}{4} \] Thus, the expression becomes: \[ \text{radians} = \frac{3\pi}{4} \]

Step 3: Calculate the Numerical Value

Using the approximation $\pi \approx 3.1416$, calculate the numerical value: \[ \text{radians} \approx \frac{3 \times 3.1416}{4} \approx 2.356 \]