Here’s a straightforward application of arccosine, that, as far as I can tell, isn’t taught too often in Precalculus and is not part of the Common Core standards for vectors and matrices.
Find the angle between the vectors and .
This problem is equivalent to finding the angle between the lines and . The angle is not drawn in standard position, which makes measurement of the angle initial daunting.
Fortunately, there is the straightforward formula for the angle between two vectors and :
We recall that is the dot product (or inner product) of the two vectors and , while is the norm (or length) of the vector .
For this particular example,
In the next post, we’ll discuss why this actually works. And then we’ll consider how the same problem can be solved more directly using arctangent.
One thought on “Inverse Functions: Arccosine and Dot Products (Part 22)”
Loved reading this thankss