SOLUTION: If sin (theta) = 8/17, find the two possible values for [tan(theta) + sec(theta)]

Question 1118937: If sin (theta) = 8/17, find the two possible values for [tan(theta) + sec(theta)]
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

$$$

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.

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