SOLUTION: Given cos theta = 24/25 and (0 < x < pi/2) Evalutate: (a) sin theta (b) sec theta

Question 27372: Given cos theta = 24/25 and (0 < x < pi/2)
Evalutate: (a) sin theta (b) sec theta
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Given cos theta = 24/25 and (0 < x < pi/2)
Evalutate: (a) sin theta (b) sec theta
since theta the angle is less than pi/2,we can think of a triangle ABC with angleABC=90 degrees or pi/2..and angle ACB =theta...so AC=hypotenuse..AB=opposite side and BC=adjacent side..so we have
cos theta=cos C =BC/AC=24/25
so BC=24 and AC =25...so from pythogarus theorem AB^2=AC^2-BC^2=25^2-24^2
=(25+24)(25-24)=49...so.....AB=7
now...sin theta = sin C = AB/AC=7/25
sec theta = sec C = AC/BC=25/24

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