15. 0/1 points details my notes larpcalclim4hs 5.3.048. find the x - intercepts of the graph. (enter your…
15. 0/1 points details my notes larpcalclim4hs 5.3.048. find the x - intercepts of the graph. (enter your answers as a comma - separated list. use n as an integer constant.) y = 6 sin πx+6 cos πx x = need help? read it watch it submit answer
Answer
Explanation:
Step1: Set y = 0
$6\sin(\pi x)+6\cos(\pi x) = 0$
Step2: Divide by 6
$\sin(\pi x)+\cos(\pi x)=0$
Step3: Rearrange the equation
$\sin(\pi x)=-\cos(\pi x)$
Step4: Use the tangent identity
$\tan(\pi x)= - 1$
Step5: Solve for x
$\pi x=-\frac{\pi}{4}+n\pi$, where $n\in\mathbb{Z}$
Step6: Isolate x
$x =-\frac{1}{4}+n$
Answer:
$x = n-\frac{1}{4},n\in\mathbb{Z}$