Question

How do you find the value for `sin2theta`, `cos2theta`, and `tan2theta` and the quadrant in which `2theta` lies given `costheta=5/13` and `theta` is in quadrant I?

Answer 1

`sin2theta=120/169 ; cos2theta=-119/169 ; tan2theta=-120/119 and 2 theta=134.76^0` lies on 2nd quadrant.

Explanation:

We know `cos theta=b/h ;sin theta=(op)/(h)`Here `b=5 ; h=13; :. op=sqrt(13^2-5^2)=12 :. sin theta=12/13 = :. sin(2theta)=2sintheta*costheta=2*5/13*12/13= 120/169 ; cos2theta=cos^2theta-sin^2theta = 25/169-144/169= -119/169 ; tan2theta=sin(2theta)/cos(2theta)=-(120/169*169/119)= -120/119`
`2theta = 134.76^0` lies on 2nd quadrant since `cos(2theta)= -119/169` as `cos2theta` is ngative in 2nd quadrant. [Ans]