Radians in 90 degrees
Understand the Problem
The question is asking to convert 90 degrees to its equivalent measure in radians. This involves using the conversion factor between degrees and radians, which is π radians equals 180 degrees.
Answer
\( \frac{\pi}{2} \)
Answer for screen readers
The final answer is ( \frac{\pi}{2} )
Steps to Solve
- Identify the conversion factor
To convert degrees to radians, use the conversion factor: $$\pi \text{ radians} = 180^{\circ}$$
- Set up the conversion formula
We need to convert 90 degrees to radians using the formula: $$\text{radians} = \text{degrees} \times \left( \frac{\pi \text{ radians}}{180^{\circ}} \right)$$
- Substitute the value
Substitute the value of 90 degrees into the formula: $$\text{radians} = 90^{\circ} \times \left( \frac{\pi \text{ radians}}{180^{\circ}} \right)$$
- Simplify the expression
Simplify the fraction: $$90 \times \left( \frac{\pi}{180} \right) = \frac{90\pi}{180} = \frac{\pi}{2}$$
Therefore, 90 degrees is equivalent to ( \frac{\pi}{2} ) radians.
The final answer is ( \frac{\pi}{2} )
More Information
π is a special mathematical constant that represents the ratio of the circumference of any circle to its diameter. It is approximately equal to 3.14159.
Tips
A common mistake is to use the wrong conversion direction or to forget to multiply by π in the numerator. Always remember: ( \text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right) ).
