Method: Trig Function Category 3

Step 1: Try Option 1: Plug It In

Step 2: Identify the Cosine Limit Identity format.

$\underset{x\to 0}{\lim }\frac{1–\mathit{cos}\left(\mathrm{(}x\mathrm{)}\right)}{x}=0$ OR $\underset{x\to 0}{\lim }\frac{x}{1–\mathit{cos}\left(\mathrm{(}x\mathrm{)}\right)}=0$

Step 3: Get the $x–\mathit{value}$outside the cosine function to match the $x–\mathit{value}$ inside the cosine function. Rewrite the equation to collect the Cosine Limit Identity pieces that now match. You want to think about this process in a similar way to finding a common denominator. You can’t multiply inside your cosine function. So, you need to multiply the outside $x–\mathit{value}$ to get the two pieces to match.

Step 4: Apply the Cosine Limit Identity and Option 1: Plug It In to solve the limit