Given #tan theta < 0#, #sin theta < 0# and #sec theta < 0#, #tan theta < 0#, which quadrants does both angles theta lie on?

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Given #tan theta < 0#, #sin theta < 0# and #sec theta < 0#, #tan theta < 0#, which quadrants does both angles theta lie on?

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Answer 1 · 2016-05-12T02:09:02

Both #tan theta and sin theta# are < 0 in the fourth quadrant Q4. Both #sec theta and tan theta# are < 0 in Q2..

Explanation:

All are > 0 for #theta# in the first quadrant #Q1(0, pi/2)#,

sine and csc only are > 0 for #theta in Q2(pi/2, pi)#,

tangent and cotangent only are > 0 for #theta in Q3(pi. (3pi)/2)# and

cosine and secant only are > 0 for #theta in Q4((3pi)/2, pi)#.

Accordingly, both #tan theta and sin theta# are < 0 in the fourth quadrant Q4.

Both #sec theta and tan theta# are < 0 in in Q2..

I have used open interval notation (..) for the intervals, owing to discontinuity-limit problems like the limits #tan (( pi/2)_(+-))=-+oo#, as #theta to pi/2#, from Q2 and Q1, respectively...

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Given #tan theta < 0#, #sin theta < 0# and #sec theta < 0#, #tan theta < 0#, which quadrants does both angles theta lie on?

1 Answer

Explanation:

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