Question

can anyone help me find the equation of the line tangent to y=4sin(x) @ x=3pi/4.

Thanks

Answer 1

The equation of the line is \(y=mx+b\), where \(m\) is the slope. You find the slope of the line by finding the derivative of your function (\(4 \sin x\)), and evaluating it at the point \(x=\dfrac{3\pi}{4}\).

Then, to find \(b\), you will need a pair of points \((x,y)\). You can do this since you know \(x=\dfrac{3\pi}{4}\) and the corresponding y-value will be found by plugging in that x-value into your function \(4\sin x\).

Then, just substitute those x and y-values into the line equation and solve for \(b\).