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

  1. Identify the conversion factor

To convert degrees to radians, use the conversion factor: $$\pi \text{ radians} = 180^{\circ}$$

  1. Set up the conversion formula

We need to convert 90 degrees to radians using the formula: $$\text{radians} = \text{degrees} \times \left( \frac{\pi \text{ radians}}{180^{\circ}} \right)$$

  1. Substitute the value

Substitute the value of 90 degrees into the formula: $$\text{radians} = 90^{\circ} \times \left( \frac{\pi \text{ radians}}{180^{\circ}} \right)$$

  1. 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) ).

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