Use the given information to find the values of the remaining five trigonometric functions. (Enter your answers in exact form.)

Question

csc x = 7/6, 0 < x < π/2

 

sin x=
cos x=

tan x=
sec x=

cot x=

Answer 1

Note: sin(x) = 1/csc(x)

         cos(x) = 1/sec(x)

         tan(x) = 1/cot(x)

 

Since, x is bounded between 0 and 90 degrees, x is an acute angle ( i.e. we we have a right triangle).

 

Thus sin(x) = 1/(7/6) = 6/7 = opp. side / hyp. The adjacent side is a² = 49 - 36 = 13, thus a = sqrt(13).

 

cos(x) = adj. side / hyp. = sqrt(13)/7

 

tan(x) = opp./adj. = 6/sqrt(13)

 

sec(x) = 1/cos(x) = 1/(sqrt(13)/7) = 7/sqrt(13)

 

cot(x) = 1/tan(x) = 1/(6/sqrt(13)) = sqrt(13)/6

 

All answers are in exact form. That is do not compute square roots.