Between x=30 degrees, and x=60 degrees, the slope of the secant to the function y=sin2x-1 is?

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lfryerda | High School Teacher | (Level 2) Educator

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The secant to a function is found by taking the average rate of change of the function between the two points given.  This means the slope of the secant is the different in y-values divided by the difference in x-values.

In this case, we have after converting `60^circ` and `30^circ` to `pi/3` and `pi/6` radians.

`m={Delta y}/{Delta x}`

`={y_2-y_1}/{x_2-x_1}`

`={(sin({2pi}/3)-1)-(sin(pi/3)-1)}/{pi/3-pi/6}`

`=6/pi((sqrt3-1)-(sqrt3-1))`

`=0`

The slope of the secant is 0. That is, the secant is a horizontal line.

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