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.