Philip P. answered • 05/25/18

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Apply the difference of two angles identity:

sin(90°-θ) = sin(90

^{o})cos(θ) - sin(θ)cos(90^{o}) =**cos(θ) = (√5)/3**Now apply the Pythagorean Identity to find sin(θ):

sin

^{2}(θ) + cos^{2}(θ) = 1 sin

^{2}(θ) + 5/9 = 1 sin

^{2}(θ) = 4/9**sin(θ) = 2/3**

tan(θ) = sin(θ)/cos(θ) = (2/3) / ((√5)/3) = (2/3)·(3/(√5)) = 2/√5

Rationalizing the denominator:

**tan(θ) =**(2/√5)·(√5/√5) =

**(2√5)/5**