The answer to this question lies in the definition of secant (sec) in trigonometry. Secant is the reciprocal of cosine (cos) and is defined as the ratio of the hypotenuse to the adjacent side of a right triangle. Since cosine has a range of -1 to 1, secant can only have a value of -1 or less. In this case, -5.2 is not a possible value for secant, thus there is no solution.
The domain of a trigonometric equation is typically limited to one period of the function. In this case, the function secant has a period of 2π, meaning that it repeats itself every 2π units. Therefore, restricting the domain to 0≤x≤2π ensures that we are only considering one full cycle of the function.
The inverse function of secant is not defined for all values of secant. It is only defined for values between -1 and 1. Since -5.2 is not a possible value for secant, we cannot use the inverse function to find more solutions.
Yes, there are ways to approximate a solution using numerical methods such as the Newton-Raphson method or the bisection method. These methods involve repeatedly evaluating the function at different values until you get close enough to the desired solution.
No, there is only one solution to this equation. As mentioned before, the range of secant is restricted to values of -1 or less, and -5.2 is not a possible value for secant. Therefore, there can only be one solution to the equation.