If cosθ=14 and θ is in Quadrant I, find sinθ

Question

.sinθ=

Answer 1

To find sinθ, we can use the Pythagorean identity sin²θ + cos²θ = 1.
Since cosθ = 14, we can square both sides to find cos²θ = 196.
Now we can substitute this into the Pythagorean identity:
sin²θ + 196 = 1.
Subtracting 196 from both sides gives us sin²θ = -195.
Since θ is in Quadrant I, sinθ is positive.
Taking the square root of both sides gives us sinθ = √(-195).
Therefore, sinθ = √195i, where i is the imaginary unit.