Question

Find an equation of the tangent line to the curve

y=sin(5x)+cos(4x)
at the point (π/6,y(π/6))
y=sin(7x)+cos(4x)
at the point (π/6,y(π/6))

Answer 1

To find the equation of the tangent line to the curve y = sin(5x) + cos(4x) at the point (π/6, y(π/6)), we need to find the derivative of the curve and substitute the given x-value. Once we have the slope, we can use the point-slope form of a line to write the equation of the tangent line.

Step-by-step explanation:

To find the equation of the tangent line to the curve y = sin(5x) + cos(4x) at the point (π/6, y(π/6)), we need to find the slope of the curve at that point. The slope of a tangent line is equal to the derivative of the function at that point. So, we start by finding the derivative of y = sin(5x) + cos(4x), which is:

dy/dx = 5cos(5x) - 4sin(4x)

Now, substitute x = π/6 into the derivative to find the slope at (π/6, y(π/6)).

After finding the slope, we can use the point-slope form of a line to write the equation of the tangent line, which is:

y - y(π/6) = slope(x - π/6)