Given that tanθ=√5/9 and sinθ is positive, determine sinθ. Write the exact answer. Do not round.

Answer 1

Well tan is opposite/adjacent. So lets make a right triangle. With an opposite side of √5 and and adjacent side of 9.

Then we can solve for the hypotenuse using the pythagorean theorem ( a²+b²=c²).

Then sin(θ)=a/h.

Answer 2

sec²θ = 1 + tan²θ = 1 + 5/81 = 86/81; cos²θ = 1/sec²θ = 81/86; sin²θ = 1 - cos²θ = 1 - 81/86 = 5/86

sinθ = √5/86 = √430/86