Question

Graph the function f(x) = -1/2 cos (-2x/3) on the graph below

Answer 1

See graph below

Step-by-step explanation:
`f(x)\text{ = }-(1)/(2)\cos ((-2)/(3)x)`

From the equation, the highest point of the graph = -0.5

y = -0.5

To p;ot the graph, we can ssign values for x, inorder to get corresponding y values

let x = -3π/2, 0, 3π/2

`\begin{gathered} \text{when x = -}(3\pi)/(2) \\ f(x)\text{ = }-(1)/(2)\cos ((-2)/(3)*\text{-}(3\pi)/(2))\text{ } \\ f(x)\text{ = }-(1)/(2)\cos (-1*\text{-}\pi)\text{ = }-(1)/(2)\cos (\pi) \\ 1\pi\text{ = 180 degr}es,\text{ }\cos (\pi)\text{ = cos 180}\degree \\ f(x)\text{ = -0.5(-1) = 0.5} \\ \\ \text{when x = 0} \\ f(x)\text{ = }-(1)/(2)\cos ((-2)/(3)*\text{0})\text{ } \\ f(x)\text{ = }-(1)/(2)\cos (0)\text{ = -0.5(1)} \\ f(x)\text{ }=\text{ -0.5} \end{gathered}`
`\begin{gathered} \text{when x = }(3\pi)/(2) \\ f(x)\text{ = }-(1)/(2)\cos ((-2)/(3)*(3\pi)/(2))\text{ } \\ f(x)\text{ = }-(1)/(2)\cos (-1*\pi)\text{ = }-(1)/(2)\cos (-\pi) \\ 1\pi\text{ = 180 degr}es,\text{ }\cos (-\pi)\text{ = cos -180}\degree \\ f(x)\text{ = -0.5( cos (-180}\degree)) \\ f(x)\text{ = 0.5} \end{gathered}`

Plotting the graph:

This graph doesn't have the same readings in its x axis as the graph you attached. It is meant as a guide on how the curve should look like

plotting the points on the given graph (sketch):