Question Bank - Mathematics

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If \(\tan ? = - \frac{5}{12},\) then what can be the value of sin ??

A.
\(\frac{5}{13}\) but cannot be \(-\frac{5}{13}\)
B.
\(-\frac{5}{13}\) but cannot be \(\frac{5}{13}\)
C.
\(\frac{5}{13}\) or \(-\frac{5}{13}\)
D.
None of the above

Solution:

Concept:Calculation:Given that, \(\tan ? = - \frac{5}{12}\) = perpendicular/BaseIn triangle ABC, using the Pythagoras theoremAC2 = AB2 + BC2? AC2 = 52 + 122 = 132? AC = 13 Hence, sin ? = perpendicular/hypotenuse? sin ? = 5/13Since tan ? is negative in 2nd and 4th quadrants.sin ? in 2nd quadrants = 5/13sin ? in 4th quadrants = - 5/13? Both 5/13 and -5/13 are possible.

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