How many radians is 90?
Understand the Problem
The question is asking how many radians are equivalent to 90 degrees. To solve this, we can use the conversion factor where 180 degrees equals π radians.
Answer
The equivalent of $90$ degrees is $\frac{\pi}{2}$ radians.
Answer for screen readers
The equivalent of $90$ degrees in radians is $\frac{\pi}{2}$.
Steps to Solve
- Identify the conversion factor
To convert degrees to radians, we use the relation that $180$ degrees is equivalent to $\pi$ radians.
- Set up the conversion
To convert $90$ degrees to radians, we can set up the equation: $$ \text{Radians} = 90^\circ \times \frac{\pi \text{ radians}}{180^\circ} $$
- Simplify the expression
Now we perform the multiplication: $$ \text{Radians} = 90 \times \frac{\pi}{180} $$ This simplifies to: $$ \text{Radians} = \frac{90\pi}{180} $$
- Calculate the final value
Further simplifying: $$ \text{Radians} = \frac{\pi}{2} $$
The equivalent of $90$ degrees in radians is $\frac{\pi}{2}$.
More Information
The conversion from degrees to radians is a common aspect of trigonometry, which is widely used in mathematics, physics, and engineering. Knowing how to convert between these two systems is essential for solving various problems involving angles.
Tips
Common mistakes include forgetting to multiply by the conversion factor or incorrectly simplifying the fraction. To avoid these mistakes, carefully follow each step of the conversion and double-check your calculations.
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