English

Find the general solution of the following equation: sin x = 1 2 - Mathematics

Advertisements
Advertisements

Question

Find the general solution of the following equation:

\[\sin x = \frac{1}{2}\]
Sum

Solution

We have:
\[\sin x = \frac{1}{2}\]
The value of x satisfying \[\sin x = \frac{1}{2}\] is \[\frac{\pi}{6}\]

∴ \[\sin x = \frac{1}{2}\]
⇒ \[\sin x = \sin\frac{\pi}{6}\]
⇒ \[x = n\pi + ( - 1 )^n \frac{\pi}{6}\]
\[n \in Z\]
shaalaa.com
  Is there an error in this question or solution?
Chapter 11: Trigonometric equations - Exercise 11.1 [Page 21]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 1.1 | Page 21

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the principal and general solutions of the equation  `cot x = -sqrt3`


Find the general solution for each of the following equations sec2 2x = 1– tan 2x


If \[\tan x = \frac{a}{b},\] show that

\[\frac{a \sin x - b \cos x}{a \sin x + b \cos x} = \frac{a^2 - b^2}{a^2 + b^2}\]

Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]


If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]


Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]


Prove that:

\[3\sin\frac{\pi}{6}\sec\frac{\pi}{3} - 4\sin\frac{5\pi}{6}\cot\frac{\pi}{4} = 1\]

 


Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]

 


Prove that

\[\left\{ 1 + \cot x - \sec\left( \frac{\pi}{2} + x \right) \right\}\left\{ 1 + \cot x + \sec\left( \frac{\pi}{2} + x \right) \right\} = 2\cot x\]

 


Prove that:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]


In a ∆ABC, prove that:
cos (A + B) + cos C = 0


Prove that:

\[\sin\frac{10\pi}{3}\cos\frac{13\pi}{6} + \cos\frac{8\pi}{3}\sin\frac{5\pi}{6} = - 1\]

Prove that:

\[\tan\frac{5\pi}{4}\cot\frac{9\pi}{4} + \tan\frac{17\pi}{4}\cot\frac{15\pi}{4} = 0\]

 


If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to


If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to


If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is

 

If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]

 

If x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =

 

Which of the following is correct?


Find the general solution of the following equation:

\[\tan x = - \frac{1}{\sqrt{3}}\]

Find the general solution of the following equation:

\[\tan x + \cot 2x = 0\]

Find the general solution of the following equation:

\[\sin 3x + \cos 2x = 0\]

Solve the following equation:

\[\sin x + \sin 2x + \sin 3 = 0\]

Solve the following equation:

\[\sin x + \sin 2x + \sin 3x + \sin 4x = 0\]

Solve the following equation:

\[\sqrt{3} \cos x + \sin x = 1\]


Solve the following equation:
\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]


Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]


If cos x = k has exactly one solution in [0, 2π], then write the values(s) of k.

 

Write the number of points of intersection of the curves

\[2y = - 1 \text{ and }y = cosec x\]

Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].


If \[\tan px - \tan qx = 0\], then the values of θ form a series in

 


The number of values of ​x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]


Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`


Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

2 cos2x + 1 = – 3 cos x


Choose the correct alternative:
If tan α and tan β are the roots of x2 + ax + b = 0 then `(sin(alpha + beta))/(sin alpha sin beta)` is equal to


Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval


Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to


Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×