Question

If the point (3/5,4/5) corresponds to an angle θ in the unit circle, what is tan θ ?

Answer 1

A point M on the unit circle could be represented by (x , y), which coordinates are nothing but cos Ф (for x) & sin Ф (for y, hence:

tan Ф = sin Ф / cos Ф ==> tan Ф (4/5) / (3/5) ==> tan Ф =(4/3).

Now let's calculate the angle: tan⁻¹Ф ==> tan⁻¹(4/3) ≈43°

Answer 2

`tan{\theta}=(4)/(3)`

Explanation:

A point M on the unit circle is represented as (x,y) for which the coordinates are
`cos{\theta}` for x and
`sin{\theta}` for y.

Now, we know that in unit circle
`tan{\theta}` is written as:

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

=
`((4)/(5))/((3)/(5))=(4)/(3)`

Thus,the value of
`tan{\theta}=(4)/(3)`.