Question

If x is an acute angle, and cos x =4/5, then cos (2 x) is equal to?

Answer 1

`cos 2x = 7/25`

Explanation:

Use trig identity:
`cos 2x = 2cos^2 x - 1`
In this case:
`cos 2x = (2)(16/25) - 1 = 32/25 - 25/25 = 7/25`
To find the sign of cos 2x, use calculator to approximately get the value of x and 2x.
`cos x = 4/5` --> `x = 36^@87` --> `2x = 73^@74`.
Since 2x is in Quadrant 1, then, cos 2x is positive.
`cos 2x = 7/25`