If cos theta= -4/9 with theta in quadrant 2, find sin theta?

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Answer 1 · 2018-02-17T14:44:00

#cos theta = (-4)/9#

We know by the identity, #sin^2theta + cos^2theta = 1#

#sin^2theta = 1 - ((-4)/9)^2#

#sin^2theta = 1 - (16/81) = 65/81#

#sintheta = +- sqrt65/9#

since #theta# lies in the second quadrant, #sintheta# must be positive,

hence, #color(darkred)(sintheta = sqrt65/9#