given cscx= -3 and tanx>0 find cosx

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  1. First identify the quadrant in which the angle lies. Since tanx>0 (posotive) it can be in either Quadrant I or III. Because sin is negative, it must be in quadrant III.

    To reach familiar terms, change cscx= -3 to sinx= -1/3 .

    Make a triangle and use sin= -1/3 to find the missing side.
    -----missing side= sqrt(8) or 2sqrt(2)

    therefore, cosx= - [2sqrt(2)]/3

    Remeber that cos is negative in Quadrant III.

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