SOLUTION: If tan y = 0.404, where y is acute, find cos2y

Question 901679: If tan y = 0.404, where y is acute, find cos2y
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if you are allowed to use a calculator, then the solution should not be difficult.
tan(y) = .404 gets you:
y = arctan(.404) = 21.99870822 degrees.
then 2y = 43.99741645 degrees.
then cos(2y) = cos(43.99741645) = .7193711228

you could also have solved it as follows:

tan(y) = .404

.404 is equivalent to 101/250

the hypotenuse of a triangle with an opposite side of 101 and an adjacent side of 250 is equal to sqrt(72701)

since this is not a rational number, we'll leave it as sqrt(72701)

so we have:

tan(y) = 101/250
cos(y) = 250/sqrt(72701)
sin(y) = 101/sqrt(72701)

by the trigonometric identity for cos(2y), you get:

cos(2y) = cos^2(y) - sin^2(y) which becomes:

cos(2y) = 250^2/72701 - 101^2/72701 = .7193711228

you get the same answer.

the 72701 in the denominator is really sqrt(72701)^2 which is equal to 72701.

for example:

(250/sqrt(72701))^2 = 250^2 / sqrt(72701)^2 = 250^2 / 72701.

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