Question

Trigonometry

Angle Sum and Difference, Double Angle and Half Angle Formulas
Find the exact value of:
If sinx = 7/9, find Cos (2x)

Answer 1

-17/81

Explanation:

cos(2x) = 1 - 2sin²x

= 1 - 2(7/9)²

= 1 - 98/81

= -17/81

Answer 2

`cos(2x)=(-17)/(81)`

Explanation:

First we have to find cosx.

We know that
`sin^2x+cos^2x=1`, so it is
`cos^2x=1-(7/9)^2=(81-49)/81=32/81`, then we have
`cosx=(4√(2))/(9)`

Then we have

`cos(2x)=cos^2x-sin^2x=((4√(2))/(9))^2-((7)/(9))^2=(32)/(81)-(49)/(81)=(-17)/(81)`