Question

If cos θ = 5/13, use the Pythagorean Identity to find sin θ.

13/13
12/13
12/5
5/13

Answer 1

sin θ=sqrt(1-cos^2 θ)
sin θ=sqrt[1-(5/13)^2]
sin θ=sqrt[1-(5)^2/(13)^2]
sin θ=sqrt[1-25/169]
sin θ=sqrt[(169-25)/169]
sin θ=sqrt(144/169)
sin θ=sqrt(144)/sqrt(169)
sin θ=12/13

Answer: Second option 12/13