How to find negative tangent - ACT Math
Card 0 of 3
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.
What is the tangent of the angle formed between the origin and the point
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 
.
Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the
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:
Compare your answer with the correct one above
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.
What is the tangent of the angle formed between the origin and the point
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 
.
Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the
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:
This is
Compare your answer with the correct one above
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 
?
What is the tangent of the angle formed between the origin and the point
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.
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.
Compare your answer with the correct one above