SOLUTION: If cos t = 3/5 and the terminal point for t is in quadrant IV, find cot t + csc t.

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Question 1180471: If cos t = 3/5 and the terminal point for t is in quadrant IV, find cot t + csc t.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

cos+%28t%29+=+3%2F5%7D%7D%0D%0A%0D%0A+and+the+terminal+point+for+%7B%7B%7Bt is in quadrant IV,
find cot%28+t%29+%2B+csc+%28t%29
recall:
cos+%28t%29+=+adj%2Fhyp=> if cos+%28t%29+=+3%2F5%7D%7D=%3E%7B%7B%7B+adj=3 and hyp=5%7D%7D%0D%0A%0D%0Athen+%7B%7B%7Bopp=sqrt%285%5E2-3%5E2%29=>opp=sqrt%2825-9%29=>opp=sqrt%2816%29=>opp=4 or opp=-4
then sin%28t%29=4%2F5 or sin%28t%29=-4%2F5
since given that the terminal point for t is in quadrant IV, sine is negative, so we will use
sin%28t%29=-4%2F5
using identities cot%28+t%29+=cos+%28t%29%2Fsin%28t%29 and csc+%28t%29=1%2Fsin%28t%29, we have
cot%28+t%29+%2B+csc+%28t%29=cos+%28t%29%2Fsin%28t%29+%2B1%2Fsin%28t%29...substitute values above
cot%28+t%29+%2B+csc+%28t%29=%283%2F5%29%2F+%28-4%2F5%29%2B1%2F%28-4%2F5%29
cot%28+t%29+%2B+csc+%28t%29=%283%2F5%2B1%29%2F%28-4%2F5%29
cot%28+t%29+%2B+csc+%28t%29=%288%2F5%29%2F%28-4%2F5%29
cot%28+t%29+%2B+csc+%28t%29=-2



Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
If cos t = 3/5 and the terminal point for t is in quadrant IV, find cot t + csc t.
matrix%281%2C7%2C+cos+%28t%29%2C+%22=%22%2C+3%2F5%2C+%22=%22%2C+A%2FH%2C+%22=%22%2C+x%2Fr%29

The above indicates a 3-4-5 Pythagorean triple, with "t" in Q IV. Therefore, y = = -4.

We then get: