Question

find the principal solution of cos theta=0°​

Answer 1

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.

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

Answer 2

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