Given that √5 tanA=-2 and CosB=8/17 in ∆ABC
State why we may assume that angle C is acute and determine the value of Sin C
Considering angles in radians for a moment:
$\tan \theta <0$ implies $\theta$ is in the second or fourth quadrants. You can remember this by the mnemonic All Students Take Calc. Starting from the first quadrant and working counter clockwise, we have
All => All (sine, cosine, and tangent are all positive in the 1st quadrant),
Students => Sine (the sine function is positive while cosine and tangent both negative in the 2nd quadrant),
Take => Tangent (the tangent function is positive while sine and cosine are both negative in the 3rd quadrant),
Calc => Cosine (the cosine function is positive while sine and tangent are both negative in the 4th quadrant)