Mark the tick against the correct answer in the following:
The value of $\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)$ is
A. $\frac{13 \pi}{6}$
B.
C. $\frac{5 \pi}{6}$
D. $\frac{\pi}{6} \frac{7 \pi}{6}$
To Find: The value of $\cos ^{-1}\left(\cos \left(\frac{13 \pi}{6}\right)\right)$
Now, let $x=\cos ^{-1}\left(\cos \left(\frac{13 \pi}{6}\right)\right)$
$\Rightarrow \cos x=\cos \left(\frac{13 \pi}{6}\right)$
Here, range of principle value of $\cos$ is $[0, \pi]$
$\Rightarrow x=\frac{13 \pi}{6} \notin[0, \pi]$
Hence for all values of $x$ in range $[0, \pi]$, the value of
$\cos ^{-1}\left(\cos \left(\frac{13 \pi}{6}\right)\right)$ is
$\Rightarrow \cos x=\cos \left(2 \pi-\frac{\pi}{6}\right)\left(\because \cos \left(\frac{13 \pi}{6}\right)=\cos \left(2 \pi-\frac{\pi}{6}\right)\right)$
$\Rightarrow \cos x=\cos \left(\frac{\pi}{6}\right)(\because \cos (2 \pi-\theta)=\cos \theta)$
$\Rightarrow x=\frac{\pi}{6}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,