Question

If x is an acute angle and tan x = 5,

The value of sin x = .
The value of cos x = .

sin x (a) 1/5
(b) 5/26
(c) 6/5

cos x (a) 1/26
(b) 6/26
(c) 3/13

Answer 1

we have that
tan x=5

we know that
tan x =sin x/ cos x
sin x/ cos x=5------> squaring-----> sin² x/cos² x=25
remember that
sin² x+cos² x=1-----> cos² x=1-sin² x
substitute
sin² x/[1-sin² x]=25
sin² x=25-25*sin² x
26*sin² x=25
sin² x=25/26
sin x=5/√26

cos² x=1-(5/√26)²----> 1-(25/26)----> 1/26
cos x=1/√26

the answers are
sin x=5/√26
cos x=1/√26