Use the definition or identities to find the exact value of

Use the definition or identities to find the exact value of each of the remaining five trigonometric functions of the acute angle theta cos theta = 1/6 sin theta = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

costheta = 1/6

sintheta = sqrt[ 1- cos^2theta]

= sqrt[ 1- 1/36] = sqrt(35)/6

tantheta = sintheta/costheta = sqrt(35)

sectheta = 1/costheta = 6

csctheta = 1/sintheta = 6/sqrt35

cot theta = 1/tan theta = 1/sqrt35