Question 1118937
i'll use x for theta.


the problem then reads:


sin(x) = 8/17, find the two possible values for (tan(x) + sec(x)


one way to solve this:


sin(x) = 8/17 means x = 28.07248694 degrees.


that's in the first quadrant.


sin(x) is positive in the first and second quadrants.


the equivalent angle in the second quadrant is 180 - 28.07248694 = 151.9275132 degrees.


the two possible values of tan(x) + sec(x) would be:


1 and 1/3 in the first quadrant and minus 1 and 1/3 in the second quadrant.


this can be seen in the following graph.


<img src = "http://theo.x10hosting.com/2018/062102.jpg" alt="$$$" >


the sine function is .471 in both equations.


that makes those 2 angles equivalent, because they have the same value for their sine function.


the tan(x) + sec(x) function is plus 1.667 in the first quadrant and minus 1.667 in the second quadrant.


i believe this is the way you solve this.


you find the angle in the four quadrants that have sine = 8/17.


those two angles were found in the first and second quadrant only.


you then find tan(x) + sec(x) for those angles.