Question 535378
find all values of t in the interval [0,2pi] satisfying |sec(t)|= squareroot 2
**
sec t=√2
t=π/4
Normally, values of t would be found only in quadrants I and IV where sec>0
But with |sec t|=√2, you must also consider |-sec t|.
When you remove the absolute value bars the equation becomes -sec t=&#8730;2 or sec t=-&#8730;2, therefore, values of t would be found as well in quadrants II and III where sec<0, as follows:
t=&#960;/4, 3&#960;/4/ 5&#960;/4 and 7&#960;/4