If the point (35,45) corresponds to an angle θ in the unit circle, what is tan θ ?
tanθ is represented by the slope of the line formed by the point and the origin.
(sinθ is the vertical distance, cosθ is horizontal distance, and tanθ = sinθ/cosθ)
slope = difference in y / difference in x
slope = 45 / 35
slope = 9 / 7
Considering the fllowing diagram:
The tangent of the angle \(\theta\) is the ratio between the length of the opposite side over the length of the adjacent side, i.e.:
\(tan( \theta)= \frac{45}{35} = \frac{9}{7}\)