SOLUTION: Find tan t given that sin t=3/5 and cot t < 0

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Question 1034092: Find tan t given that sin t=3/5 and cot t < 0
Found 3 solutions by josmiceli, stanbon, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Thinking just about signs, it is given that
sin(t) is positive and cot(t) is negative.
--------------------
The sin function is positive in the
1st and 2nd quadrants
--------------------
The cot function is negative in the
2nd and 4th quadrants
--------------------
must be an angle in the 2nd
quadrant
The horizontal component is
since
--------------------
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Find tan t given that sin t=3/5 and cot(t) is negative, t is in QII
----
Since sin = y/r, y = 3 and r = 5
----
Then x = -sqrt[5^2-3^2] = -4
-----
tan(t) = y/x = -4/5
-------------------
Cheers,
Stan H.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Find tan t given that sin t=3/5 and cot t < 0
sin is positive (> 0), and cot is negative (< 0), so t is in the 2nd quadrant. Also since cot is < 0, tan will also be < 0



Since y = 3 and r = 5, this is a 3-4-5 Pythagorean triple. Hence, x = - 4 (x is < 0 in the 2nd quadrant)

 

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