## Example Questions

### Example Question #26 : Trigonometry

What is the tangent of the angle formed between the origin and the point if that angle is formed with one side of the angle beginning on the -axis and then rotating counter-clockwise to ?      Explanation:

You can begin by imagining a little triangle in the second quadrant to find your reference angle. It would look like this: The tangent of an angle is: For our data, this is: Now, since this is in the second quadrant, the value is negative, given the periodic nature of the tangent function.

### Example Question #27 : Trigonometry

What is the tangent of the angle formed between the origin and the point if that angle is formed with one side of the angle beginning on the -axis and then rotating counter-clockwise to ? Round to the nearest hundredth.      Explanation:

Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the -axis as your reference point for your angle. (Hence, it is called the "reference angle.")

Now, it is easiest to think of this like you are drawing a little triangle in the second quadrant of the Cartesian plane. It would look like: So, the tangent of an angle is: or, for your data, .

This is . Rounding, this is . However, since is in the second quadrant, your value must be negative. (The tangent function is negative in that quadrant.) Therefore, the answer is .

### Example Question #28 : Trigonometry

What is the tangent of the angle formed between the origin and the point if that angle is formed with one side of the angle beginning on the -axis and then rotating counter-clockwise to ? Round to the nearest hundredth.      Explanation:

Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the -axis as your reference point for your angle. (Hence, it is called the "reference angle.")

Now, it is easiest to think of this like you are drawing a little triangle in the fourth quadrant of the Cartesian plane. It would look like: So, the tangent of an angle is: or, for your data, or . However, since is in the fourth quadrant, your value must be negative. (The tangent function is negative in that quadrant.) This makes the correct answer . 