Solving Problems Involving Tangent Functions

The calculator must be set to radians (RAD) when working with trigonometric functions.

1. Identify the variables.

2. Place the information on the Cartesian plane and sketch the curve.

3. Find the rule of the function.

4. Answer the question(s).

Since tangent functions are periodic, there are many possible $x$ values for any given $y$ value.

Enya is participating in a drone competition that requires her to perform a number of maneuvers. One of them follows a trajectory corresponding to a tangent function. The height of the drone is determined as a function of the horizontal distance between the drone and the competitor.

Here are the details of this trajectory:

• At $11$ metres high, the drone must be $9.38$ metres away horizontally.

• At a height of $15$ metres, the drone must be approximately $10.65$ metres away horizontally.

• Enya must be situated at the origin of the Cartesian plane.

• $11$ metres from the competitor, there is a building along which the drone must fly.

a) What is the height of the drone when it is $2$ metres away horizontally?

b) What horizontal distance did the drone travel when it is at a height of$12$ metres?

c) If Enya’s drone is $1$ metre away horizontally and $8$ metres high, is she successfully following the trajectory?