Converting Degrees to Radians: $270^{\circ}$
To convert an angle from degrees to radians, we use the conversion factor $\frac{\pi \text{ radians}}{180^{\circ}}$.
Calculation Steps
-
Multiply the angle in degrees by the conversion factor:
$ 270^{\circ} \times \frac{\pi \text{ radians}}{180^{\circ}} $
-
Simplify the expression:
$ \frac{270}{180} \times \pi \text{ radians} $
-
Reduce the fraction $\frac{270}{180}$. Both numerator and denominator are divisible by 90:
$ \frac{270 \div 90}{180 \div 90} = \frac{3}{2} $
-
The result is:
$ \frac{3}{2} \pi \text{ radians} $
Final Answer
Therefore, the radian measure of $270^{\circ}$ is $\frac{3\pi}{2}$.
Similar Questions
A sector has a central angle of 135° and a radius of 8 cm. Another sector of the same circle has a central angle of \(\dfrac{3\pi}{4}\) radians. What is the ratio of the area of the first sector to the area of the second sector?
Convert 2.5 radians to degrees.
A sector of a circle having a radius of 10 cm and has a central angle of \(\frac{3\pi}{4}\) radians. What is the area of the sector?
- Convert 0.5 radians to degrees.
Convert \(\frac{2\pi}{3}\) radians to degrees.
What is \(\frac{3\pi}{4}\) radians in degrees?
- Convert 1.5 radians to degrees.
What is the radian measure of 150°?
What is \(\dfrac{5\pi}{4}\) radians in degrees?
- Convert 3 radians to degrees.
Important Questions from Angles and measures in degrees and radians
If P = sin20 θ + cos48 θ, then the inequality that holds for all values of θ is
Express \({\pi\over 12}\) radians in degrees.
- Which of the following angles is same as 135° ?
- Which of the following is the best approximated degree measure of 4 radians?
30 degree is equal to _________ radians.
