find the principal solution of cos theta=0°
Answers
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
Since the trigonometric functions are periodic, therefore, if a trigonometric equation has a solution, it will have infinitely number of solutions.
For example,
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.
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