SOLUTION: sec(x)=radical 5 with sinx>0, find tan(2x)

Algebra ->  Trigonometry-basics -> SOLUTION: sec(x)=radical 5 with sinx>0, find tan(2x)      Log On


   

Question 873344: sec(x)=radical 5 with sinx>0, find tan(2x)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
sec(x)=radical 5 with sinx>0, find tan(2x)
Given reference angle x is in quadrant I
secx=sqrt%285%29
cosx=1%2Fsecx=1%2Fsqrt%285%29=sqrt%285%29%2F5

tanx=sinx%2Fcosx=sqrt%2820%29%2Fsqrt%285%29=sqrt%284%29=2
Identity: tan%282x%29=%282tanx%29%2F%281-tan%5E2%28x%29%29=4%2F%281-4%29=4%2F-3=-4%2F3
Calculator check:
cosx=√5/5
x≈63.43˚
2x≈126.86˚
tan 2x≈tan(126.86)≈-1.333…
exact value as calculated above=-4/3≈-1.333…