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
- If $\sin(3x - 20)^\circ = \cos(20 - 3y)^\circ$, then value of x - y will be:
- If $(1 + \tan A)(1 + \tan B) = 2$, then what will be the value of $\tan(A+B)$?
- The value of $\frac{\tan 45^\circ - \tan 30^\circ}{1 + \tan 45^\circ \tan 30^\circ}$ is :
- If $\cos\theta + \sec\theta = \sqrt{3}$, then the value of $\cos^3\theta + \sec^3\theta$ is:
- If $x + y = 75$ and $\sin x : \sin y = \frac{1}{\sqrt{2}} : \frac{1}{2}$, then $x : y$ is:
- If $\sin \theta + \text{cosec } \theta = \sqrt{5}$, then the value of $\sin^3 \theta + \text{cosec}^3 \theta$ is:
- If $\cot 3\theta \cot 6\theta = 1$, then the value of $\tan 15\theta$ will be:
- If $\cos x + \frac{1}{\cos x} = 2$ then find the value of $\cos^n x + \frac{1}{\cos^n x}$
- If $a \tan \alpha = b$, then the value of $\cos \alpha$ will be:
- If $\sin\theta - \cos\theta = \frac{\sqrt{3}}{2}$, then find the positive value of $\sin\theta + \cos\theta$.
Important Questions from Trigonometry
(secθ + tanθ)/(secθ - tanθ) is equal to:
If tan 45°, cot θ then the value of θ, in radians is
ABC is a triangle If sin (A+B)/2 = √3/2, then the value of sin C/2 is
The angles of elevation of the top of a temple, from the foot and the top of a building 30 m high, are 60° and 30° respectively. Then height of the temple is
what is the principal value of \(\sin^{-1} \left( \sin \dfrac{2 \pi}{3} \right)\) ?
