Question

5. Find cos theta if sin theta= -12/13
and tan theta > 0. (6 points)

Answer 1

`\text{Given that,}\\\\\sin \theta = -(12)/(13)\\\\\implies \sin^2 \theta = (144)/(169)\\\\\implies 1- \cos^2 \theta = (144)/(169)\\\\\implies \cos^2 \theta = 1- (144)/(169)\\\\\implies \cos^2 \theta = (25)/(169)\\\\\implies \cos \theta = \pm \sqrt{(25)/(169)} = \pm \frac 5{13}\\\\\\\text{Since,}~ \tan \theta >0,\\\\\cos \theta =- (5)/(13)`