SOLUTION: Please help me chose the correct answer. Given sin(θ)=(3sqrt(17))/17, use the Pythagorean identity to find all possible values for tan(θ). a) -sqrt(34)/17 b) sqrt(

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Question 1085034: Please help me chose the correct answer.
Given sin(θ)=(3sqrt(17))/17, use the Pythagorean identity to find all possible values for tan(θ).
a) -sqrt(34)/17
b) sqrt(34)/17
c) -(2sqrt(34))/17
d) -(3sqrt(2))/4
e) (3sqrt(2))/4
f) (2sqrt(34))/17
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%28+3%2Asqrt%2817%29%29+%2F+17+=+3+%2F+sqrt%2817%29+
( dividing both sides by +sqrt%2817%29+ )
+%28+sqrt%2817%29+%29%5E2+=+3%5E2+%2B+b%5E2+
+17+=+9+%2B+b%5E2+
+b%5E2+=+8+
+b+=+2%2Asqrt%282%29+
-----------------------
+tan%28+theta+%29+=+a%2Fb+ where:
+a+=+3+
+b+=+2%2Asqrt%282%29+
+tan%28+theta+%29+=+3+%2F+%28+2%2Asqrt%282%29+%29+
Multiply top and bottom by +sqrt%282%29+
+tan%28+theta+%29+=+%28+3%2Asqrt%282%29+%29+%2F+4+
-----------------------------------
+sin%28+theta+%29+is+positive%2C+which+means+%7B%7B%7B+theta+ can
only be in the 1st or 2nd quadrant. If +theta+ is in
the 2nd quadrant, then +b+=+-2%2Asqrt%282%29+
and you must multiply top and bottom of
+3+%2F+%28+-2%2Asqrt%282%29+%29+ by +-sqrt%282%29+, and you get
+tan%28+theta+%29+=+-%28+3%2Asqrt%282%29+%29+%2F+4+
----------------------------------
I conclude that the answer can be either d) or e)
You may want a 2nd opinion on this