Angle Conversion: Degrees to Radians
To convert an angle from degrees to radians, we use the conversion factor $\frac{\pi}{180^\circ}$.
The given angle is $54^\circ$. Applying the conversion formula:
$ 54^\circ \times \frac{\pi}{180^\circ} $
Simplifying the Expression
We need to simplify the fraction $\frac{54}{180}$. Both 54 and 180 are divisible by their greatest common divisor, which is 18.
- Divide the numerator by 18: $54 \div 18 = 3$
- Divide the denominator by 18: $180 \div 18 = 10$
Therefore, the expression simplifies to:
$ \frac{3\pi}{10} $
Final Answer
The angle $54^\circ$ is equivalent to $\frac{3\pi}{10}$ radians. This corresponds to Option 3.
Similar Questions
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Important Questions from Trigonometry
The given equation can be reduced to
If sin2x = a - b√c, where a and b are natural numbers and c is prime number, then what is the value of a - b + 2c ?
If \(\sin θ = \frac{8}{{17}}\) , then find the value of tan θ.
If cos(A - B) = \(\frac{\sqrt 3}{2}\) and cot(A + B) = \(\frac{1}{\sqrt 3}\) , Where A - B and A + B are acute angles, then (2A - 3B) is equal to:
If 3 tanθ = \(2\sqrt 3 \) sinθ, 0° < θ < 90°, then the value of \(\rm \frac{{\cos e{c^2}2\,\theta + {{\cot }^2}2\,\theta }}{{{{\sin }^2}\,\theta + {{\tan }^2}2\,\theta }}\) is:
