Question

Someone please answer it’s 50 points!!

Answer 1

Hello!

Let's consider what the question asks for:

==> equation of tangent line to y = 3sin(x)

--> at: x = 5π/4

To find the slope of the line at a specific point on the function

--> MUST find the derivative of equation

`(d)/(dx) 3sin(x)=3cos(x)`

Derivative is function to find slope of function at every specific point

--> let's find the slope at x = 5π/4

`3cos(x)=3*cos((5\pi )/(4) )=3*(-(√(2) )/(2) )=-(3√(2) )/(2)`

Now that we found the slope, we must also find the point at which the tangent line touches the function

--> simply plug x = 5π/4' to find y

`y=3sin((5\pi )/(4) )=-(3√(2) )/(2)`

--> thus our point which the tangent line and function touch is

`((5\pi )/(4),-(3√(2) )/(2) )`

Now let's write our tangent line's equation in point-slope form:

`y+(3√(2) )/(2) =-(3√(2) )/(2) (x-(5\pi )/(4))` <== Answer