Consider the Function y=2cosx+5 Calculate the exact value(s) of x for which the slope of the tangent to the graph is 1 on the interval 0≤x≤2π

Question

Consider the Function y=2cosx+5 Calculate the exact value(s) of x for which the slope of the tangent to the graph is 1 on the interval 0≤x≤2π

Answer 1

y = 2 cos x + 5

y' = - 2 sin x

y' = -2 sin x =1 when sin x = -1/2

Since the value of sine is negative we check the 3rd and 4th quadrants.

sin x = 1/2 when x = π/6 so sin x = -1/2 when x = π + (π/6) = 7π/6) and 2π - (π/6) = 11π/6

Answer 2

Hello Mikayla,

To find those x-values, you would need to:

1. find y', the derivative of y
2. set it equal to 1 and solve for x-values on 0≤x≤2π

So: y' = -2 sinx

Set it equal to 1 and solve for x-values on 0≤x≤2π: -2sinx = 1 ---> sin x = -1/2

The solutions are 7π/6 (Quadrant 3) and 11π/6 (Quadrant 4)