Question

The point P(12, 16) is on the terminal side of θ. Evaluate tan θ.

Answer 1

Ok, so given terminal side, we are given the coordinates (12,16), but we are also given another piece of information. Because terminal side means that the line has been rotated. In this case, the line has been rotated counterclockwise, as it has moved from the x axis to the first quadrant. Now the point (12,16) is an essential piece to this. From the origin (0,0), create a straight line to (12,16) to create a hypotenuse of the triangle. This way, it is easier to see why you use trig functions. Then you connect the point (0,16) to (12,16). After drawing the triangle, you know what the dimensions are for both legs, which are given by the problem. Just label those dimensions onto the triangle. Now as for trig functions, recall how to find them. You can use SOH CAH TOA to figure out what dimensions to set equal to the angle measurement. Sin is opposite over hypotenuse, cos is adjacent over hypotenuse, and tan is opposite over adjacent. Opposite simply refers to measurements that run vertically (y values), while adjacent refers to measurements that run horizontally (x values). The syntax to input on a calculator is tanθ = opposite/adjacent. You can do the rest. One last note. Remember that if you're finding an angle measure in degrees or radians, check the "mode" of the calculator and set them to either of those, as they will have drastically different answers.

Answer 2

Oh yeah, I meant the syntax for tan in general is tanθ = opposite/adjacent, not syntax for a calculator. Also, once you have plugged in the unknown variables into the function, simply just use the arctan function (tan^-1), as they find angles based on dimensions.

Answer 3

Well explained @InsatiableSuffering (:

Answer 4

I actually goofed up my explanation lol

Answer 5

I meant to say "connect (12,0) to (12,16)"

Answer 6

lol it happens. Still nice job (: