Question

Find the acute angle between the tangent line to r1(t) and r2(t)

A) The acute angle depends on the specific functions of r1(t) and r2(t).
B) The acute angle is always 45 degrees.
C) Tangent lines do not have acute angles.
D) The acute angle is determined by the difference in slopes.

Answer 1

The acute angle between the tangent lines to r1(t) and r2(t) can be found by finding the difference in slopes of the two curves and taking the inverse tangent of that value.

Step-by-step explanation:

The acute angle between the tangent line to r1(t) and r2(t) can be determined by finding the difference in slopes of the two curves. The tangent lines to the curves represent the instantaneous rate of change at a specific point. The acute angle between these tangent lines can be found by finding the difference in slopes and taking the inverse tangent of that value.

Let m1 be the slope of the tangent line to r1(t) and m2 be the slope of the tangent line to r2(t). The acute angle between the two tangent lines is given by:

angle = arctan(|m1 - m2|)