SOLUTION: Tan y =2 find cos y

Question 1203568: Tan y =2 find cos y

Found 3 solutions by ikleyn, greenestamps, MathLover1:
Answer by ikleyn(52914)   (Show Source): You can put this solution on YOUR website!
.
tan(y) =2. Find cos(y).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Having given tan(y) = 2, we can imagine a right-angled triangle with acute angle "y", the adjacent leg of the length 1 and the opposite leg of the length 2. Then the hypotenuse length is = and cos(y) = = . ANSWER

Solved.

Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!

I'm changing the angle name from y to theta so I can discuss the problem in terms of x, y, and the magnitude r.

Given , there are two possibilities:

(1) the angle is in quadrant I with y=2, x=1 and . In this case,

(2) the angle is in quadrant III with y=-2, x=-1 and . In this case,

ANSWERS: or

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

find
use trigonometric identities

Pythagorean trigonometric identity

then

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