Question 706379: Find sine and cosine of each of the following.
2x, given tan(x)=3, sin(x)<0
Thank You very much.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find sine and cosine of each of the following.
2x, given tan(x)=3, sin(x)<0
**
we are working with a reference angle in quadrant III where tan>0, sin<0 and cos<0
let O=opposite side
let A=adjacent side
let H=hypotenuse
Given tanx=3=O/A=3/1
O=3, A=1
H=√(O^2+A^2)=√(3^2+1^2)=√(9+1)=√10
sinx=O/H=-3/√10
cosx=A/H=-1/√10
..
sin2x=2sinxcosx
=2(-3/√10)(-1/√10)
=6/10
=3/5
..
cos2x=cos^2x-sin^2x
=(-3/√10)^2-(-1/√10)^2
=9/10-1/10
=8/10
=4/5
|
|
|
