SOLUTION: Can a given angle &#945; satisfy both cos &#945; > 0 and sec &#945; < 0? Explain? If, for some particular angle &#952;, sec &#952;< 0 and csc &#952; <0, in what quadrant must &#

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Question 1049961: Can a given angle α satisfy both cos α > 0 and sec α < 0? Explain?
If, for some particular angle θ, sec θ< 0 and csc θ <0, in what quadrant must θ lie? What is the sign of cotθ>?
Found 3 solutions by Alan3354, stanbon, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Can a given angle satisfy both cos > 0 and sec < 0? Explain?
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Yes. eg, angle = 45 degs
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If, for some particular angle x, sec x < 0 and csc <0, in what quadrant must x lie?
Q3
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What is the sign of cot? Depends on which quadrant.
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Can a given angle α satisfy both cos α > 0 and sec α < 0? Explain?
Ans: No, because sec is the multiplicative inverse of cos
sec(t) = 1/cos(t)
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If, for some particular angle θ, sec θ< 0 and csc θ < 0, in what quadrant must θ lie? What is the sign of cotθ>
If sec(t) < 0, t is in QII or QIII
If csc(t) < 0, t is in QIII or QIV
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Ans: t is in QIII
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Ans: cot(t) = cos(t)/sin(t) = (1/sin)(1/sec) = csc*(1/sec) = -*(1/-) = +
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Cheers,
Stan H.
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Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.
Can a given angle α satisfy both cos α > 0 and sec α < 0? Explain?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

 = , by the definition.


So, if  > , then  > 0.


And vice versa.


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