Question

P (x,y) is the point of the unit circle determined by real number Theta, tan theta equals

A. x/y
B. y/x
C. 1/x
D. 1/y

Answer 1

Option B.

Explanation:

By definition, the tangent of an angle is equal to

`tan \theta = \frac {sin \theta}{cos \theta}`

We can replace sin and cos by their definitions

`tan \theta = \frac {\frac {opposite}{hipotenuse}} {\frac {adjacent}{hipotenuse}}`

As we can check on the attached image, we are working on the unit circle, the hypotenuse is 1, the opposite side is y and the adjacent side is x. We can replace this on the formula above to get...

`tan \theta= \frac {\frac {opposite}{hipotenuse}} {\frac {adjacent}{hipotenuse}} = \frac {(y)/(1)}{(x)/(1)}`

Finally, simplifying we get the final result...

`tan \theta= \frac {\frac {opposite}{hipotenuse}} {\frac {adjacent}{hipotenuse}} = \frac {(y)/(1)}{(x)/(1)} = (y)/(x)`

Answer 2

On the unit circle, tan (theta) = y/x.