Evaluate the expression. Assume that all angles are in quadrant 1.
1. cos(arccos4/5)
by definition,
arccos(4/5) is the angle whose cosine is 4/5
so, cos(that angle) is . . . 4/5!
To evaluate the expression cos(arccos(4/5)), we can use the fact that the cosine function is the inverse of the arccosine function.
The arccosine function, also known as inverse cosine function, takes an input between -1 and 1 and gives the angle whose cosine is the given value. In this case, arccos(4/5) gives the angle whose cosine is 4/5.
We know that cos(arccos(x)) = x for any value of x between -1 and 1. So we can directly substitute 4/5 for x in the expression cos(arccos(x)).
cos(arccos(4/5)) = 4/5
Therefore, the value of the expression cos(arccos(4/5)) is 4/5.