Use the properties of inverse functions to find the exact value of c.pdf

Use the properties of inverse functions to find the exact value of cos^-1(cos7pi/4).
Solution
Note that:
arccos[cos(x)] = x for 0 < x <= pi.
However, since pi < 7pi/4, the property is not yet applicable.
Since the period of cosine is 2pi, we see that:
cos(7pi/4) = cos(7pi/4 - 2?) = cos(-pi/4) = cos(pi/4).
Since 0 < pi/4 <= pi, we see that:
arccos[cos(7pi/4)] = arccos[cos(pi/4)] = pi/4. ANSWER.

1. Use the properties of inverse functions to find the exact value of cos^-1(cos7pi/4).

Solution

Note that:

arccos[cos(x)] = x for 0 < x <= pi.

However, since pi < 7pi/4, the property is not yet applicable.

Since the period of cosine is 2pi, we see that:

cos(7pi/4) = cos(7pi/4 - 2?) = cos(-pi/4) = cos(pi/4).

Since 0 < pi/4 <= pi, we see that:

arccos[cos(7pi/4)] = arccos[cos(pi/4)] = pi/4. ANSWER