For tan x24 anjd find the value of sin x and cos xSolutionta

For tan x=2/4 anjd find the value of sin x and cos x.

Solution

tanx = 2/5 and x E [ , 3/2] ( third quadrant)

in the given interval sine and cosine functions are negative

tanx = 2/5 = opposite side / adjacent side

==> opposite side = 2 , adjacent side = 5

==> from pythagorous theorem hypotenuse² = 2² + 5² = 29

==> hypotenuse = 29

sinx = opposite side / hypotenuse = -2/29

cosx = adjacent side / hypotenuse = -5/29