CBSE BOARD XII, asked by tarunrao670, 3 months ago

find the principal solution of cos theta=0°​

Answers

Answered by diajain01
118

QUESTION⤵️

find the principal solution of cos theta=0°

ANSWER⤵️

The solutions lying between 0 to 2π or between 0° to 360° are called principal solutions.

Consider the equation 2 cos θ + 1 = 0 or cos θ = -1/2. This equation is clearly, satisfy by

theta =  \frac{2\pi}{3} . \:  \:  \frac{4\pi}{3} \:  etc

Since the trigonometric functions are periodic, therefore, if a trigonometric equation has a solution, it will have infinitely number of solutions.

For example,

θ =  \frac{2\pi}{3} , 2π ±  \frac{2\pi}{3} , 4π ±  \frac{2\pi}{3} ,

etc are solutions of 2 cos θ + 1 = 0.

These solutions can be put together in compact form as 2nπ ± 2π/3 where n is an integer.

This solution is known as the general solution.

Thus, a solution generalize by means of periodicity is known as the general solution.

\huge\star\mathtt\red{hope \:  it  \: helps}\star


tarunrao670: thnx...
diajain01: :)
Answered by theherosaharsh1234
4

question is the find the principal solution of cos theta=0

Similarly, general solution for cos x = 0 will be x = (2n+1)π/2, n∈I, as cos x has a value equal to 0 at π/2, 3π/2, 5π/2, -7π/2, -11π/2

Similar questions