If cos x=1/4 and 0 <x< 90°, find tan x.
Let's first use the Pythagorean identity to find sin x:
sin^2 x + cos^2 x = 1
sin^2 x + (1/4)^2 = 1
sin^2 x = 15/16
sin x = sqrt(15)/4
Now, we can use the definition of tangent to find tan x:
tan x = sin x / cos x
tan x = (sqrt(15)/4) / (1/4)
tan x = sqrt(15)
Therefore, tan x = sqrt(15).
If sinx =2/3 and 0° < x < 90°, find cos x.
Again, we can use the Pythagorean identity to find cos x:
sin^2 x + cos^2 x = 1
(2/3)^2 + cos^2 x = 1
cos^2 x = 5/9
cos x = sqrt(5)/3
Therefore, cos x = sqrt(5)/3.