SOLUTION: Let θ be an angle in quadrant II such that secθ=-(13)/(12) Find the exact values of cotθ and sinθ...

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Question 586488: Let θ be an angle in quadrant II such that secθ=-(13)/(12)
Find the exact values of cotθ and sinθ...

Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Let θ be an angle in quadrant II such that secθ=-(13)/(12)
Find the exact values of cotθ and sinθ...
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In QII x is negative and y is positive.
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sec(theta) = r/x = -13/12 implies that r = 13 and x = -12
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Then y^2 = 13^2-12^2 = 169-144 = 25
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y = +5
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sin = y/r = 5/13
cos = x/r = -12/13
tan = y/x = -5/12
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csc = r/y = 13/5
sec = -13/12
cot = -12/5
===============
Cheers,
Stan H.
===============

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Secant is just the reciprocal of cosine, so if



then



which is just fine because cosine is negative in Quadrant II.

Then use the Pythagorean identity:



from which we can derive:



And you choose based on the quadrant.

For you, sine is positive in QII, so:



John

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