Using double-angle identities

[AlexDoesMath]

Given: cos x = 4/11 and x is in Quadrant I.
Find the exact values of sin(2x), cos(2x), tan(2x). Don’t need to solve for x.

 

[Deleted member 4993]

Given: cos x = 4/11 and x is in Quadrant I.
Find the exact values of sin(2x), cos(2x), tan(2x). Don’t need to solve for x.

Can you express cos(2x) in terms of cos(x)?

 

[tkhunny]

1) Draw a right triangle.
2) Label an angle "x".
3) Label the adjacent side and hypotenuse "4" and "11":.
4) Calculate and label the length of the Opposite side.
5_ Express all your target functions (2x versions) in terms for their "1x" brothers.

You're almost done. Don't forget the SIGN of the "2x" functions might be different from their "1x" sisters..

 

[pka]

1. Given: cos x = 4/11 and x is in Quadrant I. Find the exact values of sin(2x), cos(2x), tan(2x). Don’t need to solve for x.

Given \(\cos(\theta)=t\) and \(\theta\in I \) then \(\sin(\theta)=\sqrt{1-\cos^2(\theta)}\).
Moreover, \(\sin(2\theta)=2\sin(\theta)\cdot\cos(\theta),~\cos(2\theta)=2\cos^2(\theta)-1,~\&~\tan(2\theta)=\dfrac{\sin(2\theta)}{\cos(2\theta)}\)