SOLUTION: Find sin (2x), cos (2x), and tan (2x) from the given information. tan (x) = 1/2 x in quadrant 1

Algebra ->  Trigonometry-basics -> SOLUTION: Find sin (2x), cos (2x), and tan (2x) from the given information. tan (x) = 1/2 x in quadrant 1      Log On


   

Question 810475: Find sin (2x), cos (2x), and tan (2x) from the given information.
tan (x) = 1/2
x in quadrant 1
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find sin (2x), cos (2x), and tan (2x) from the given information.
tan (x) = 1/2, x in quadrant I
***
Hypotenuse of reference right triangle in quadrant I=√(1^2+2^2)=√5
sinx=1/√5
cosx=2/√5
tanx=1/2
..
sin(2x)=2sinxcosx=2*1/√5*2/√5=4/5
cos(2x)=cos^2x-sin^2x=4/5-1/5=3/5
tan(2x)=(2tanx)/(1-tan^2x)=1/(1-1/4)=1/(3/4)=4/3