If x is an acute angle of a right trangle and secx=7/5, use SOHCAHTOA to find (3sinx+4cosx)/(tanx-cotx). simplify completely, rationalizing all denominators. (*I mostly need help with simplifying the expression and rationalizing).

Question

amistre64 · Answer

there is no sohcahtoa in math ....

amistre64 · Answer

sec x=7/5
cos x = 5/7
sin x = sqrt(1-(25/49))
tan x = sinx/cosx

amistre64 · Answer

cot = 1/tan

anonymous · Answer

so far i have secx=7/5, therefore cosx= 5/7. sinx=2radical6/7, csc=7radical6/12. and tanx=2radical6 over 5, and cot=5radical6/12

amistre64 · Answer

those look good

anonymous · Answer

plugging it into the equation is where i'm stuck. my issue is rationalizing all the radicals.

amistre64 · Answer

tanx=2sqrt(6)/5

cot=5/2sqrt(6) ... yeah, same thing

anonymous · Answer

|dw:1315684614448:dw|
5^2 + n^2 = 7^2
n^2 = 49 - 25
n = sqrt(24)

sinx = 2sqrt(6)/7
cosx = 5/7
tanx = 2sqrt(6)/5