Question

solve x
using cos trignomertry

Answer 1

Answer:

The equations containing trigonometric functions or t-ratios of an unknown angle or real number are known as trigonometric equations.

examples:

cos x = ½, sin x = 0, tan x = √3 etc. are trigonometric equations.

solution of trigonometric equation:

A solution of a trigonometric equation is the value of the unknown angle that satisfies the equation.

Consider the equation sin θ = ½. This equation is, clearly, satisfied by θ = π/6, 5π/6 etc. so these its solution. Solving an equation means to find the set of all values of the unknown value which satisfy the given equation.

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 θ = 2π/3, 4π/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 = 2π/3, 2n ± 2π/3, 4n ± 2π/3, ………… 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.

Note-general soluton is not restricted to only 0 to 2π.