Question

Find the equation of the tangent line to the curve y = 4sin x at the point (pi/6, 2) .

Answer 1

Step 1

`\begin{gathered} y=4sinx \\ \\ (dy)/(dx)\text{ = 4cosx} \\ \\ (\pi)/(6)\text{ = 30} \\ \\ m\text{ = 4cos30} \\ \\ m\text{ = 2}√(3) \end{gathered}`

Step 2

`\begin{gathered} y\text{ -2 = 2}√(3)\text{ \lparen x-}(\pi)/(6)) \\ \\ y\text{ - 2 = 2}√(3)x\text{ - }(\pi√(3))/(3) \\ \\ y\text{ = 2}√(3)x\text{ + 2 - }(\pi√(3))/(3) \\ \\ b\text{ = 2 - }(\pi√(3))/(3) \end{gathered}`
`\begin{gathered} m\text{ = 2}√(3) \\ \\ b\text{ = 2 - }(\pi√(3))/(3) \end{gathered}`