Question

If sin A = 1/√10 with A in QII find cos 2A.

Answer 1

cos(2A) = 4/5

Explanation:

Since A is in QII, then
`\cos A < 0`

`\displaystyle \sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=(1)/(√(10))\\\\\cos A=\frac{\text{Adjacent}}{\text{Hypotenuse}}=\frac{\sqrt{√(10)^2-1^2}}{√(10)}=(√(10-1))/(√(10))=(√(9))/(√(10))=(-3)/(√(10))`

Therefore:

`\displaystyle \cos 2A=\cos^2A-\sin^2 A=\biggr((-3)/(√(10))\biggr)^2-\biggr((1)/(√(10))\biggr)^2=(9)/(10)-(1)/(10)=(8)/(10)=(4)/(5)`