question: find the general solution (in radians) of the trigonometric equation below for all real values of…

question: find the general solution (in radians) of the trigonometric equation below for all real values of x, expressing your answer in terms of k as determined by the dropdown below. sec x + 4 = 3 answer: attempt 1 out of 2 use the button below to add a second expression if necessary. x =

question: find the general solution (in radians) of the trigonometric equation below for all real values of x, expressing your answer in terms of k as determined by the dropdown below. sec x + 4 = 3 answer: attempt 1 out of 2 use the button below to add a second expression if necessary. x =

Answer

Explanation:

Step1: Rewrite secant in terms of cosine

Recall that $\sec x=\frac{1}{\cos x}$. So the equation $\sec x + 4=3$ becomes $\frac{1}{\cos x}+4 = 3$.

Step2: Isolate the cosine - term

Subtract 4 from both sides of the equation: $\frac{1}{\cos x}=3 - 4=-1$. Then, cross - multiply to get $\cos x=-1$.

Step3: Find the general solution of the cosine equation

The general solution of the equation $\cos x = a$, where $|a|\leq1$, is given by $x = 2k\pi\pm\cos^{-1}(a)$, $k\in\mathbb{Z}$. Since $\cos x=-1$, and $\cos^{-1}(-1)=\pi$, the general solution is $x=(2k + 1)\pi$, $k\in\mathbb{Z}$.

Answer:

$x=(2k + 1)\pi$