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Question:

If \u03B8 is an obtuse angle and $5193_w106_h41.png$ in Quadrant III, what is $6421_w242_h18.png$?

A $1611_w58_h42.png$
Explaination

Use the trigonometric identity $7460_w149_h18.png$ to solve for $9040_w46_h17.png$, then use the Quadrant information to solve for $7700_w39_h13.png$, which can then be used to find $6739_w50_h17.png$ and $9214_w40_h12.png$.
Substitute the $9580_w41_h12.png$ into the trigonometric identity:
$3089_w163_h41.png$, which becomes
$8022_w111_h38.png$, so $9216_w81_h38.png$.
Evaluate the square root to find sin\u03B8:
$7357_w181_h45.png$. It is given that the cosine value is in Quadrant III, so the sine value is negative and equals $2572_w24_h37.png$.
Recall that $8326_w110_h37.png$ and $1683_w107_h37.png$. Substitute the appropriate values to find tangent and secant:
$8243_w182_h52.png$