Use the definition or identities to find the exact value of each of the remaining five trigonometric functions of the acute angle thetaθ. sine theta equals startfraction startroot 5 endroot over 6 endfractionsinθ= 5 6

Sine angle represents opposite over hypotenuse. 
Use the Pythagorean Theorem to find the adjacent side.
(√5)² + x² = 6²  → 5 + x² = 36  → x² = 31 → x = √31

sin Ф = √5/6                                         csc Ф = hyp/opp = 6/√5 = 6√5/5
cos Ф = adj/hyp = √31/6                      sec Ф = hyp/adj = 6/√31 = 6√31/31
tan Ф = opp/adj = √5/√31 = √155/31    cot Ф = adj/opp = √31/√5 = √155/5

This is in Quadrant I.  If the coordinates are in Quadrant II, then "adj" will have a negative sign.
 

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