ACT Math : How to find negative tangent

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #21 : Tangent

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 ?

Possible Answers:

Correct answer:

Explanation:

You can begin by imagining a little triangle in the second quadrant to find your reference angle. It would look like this:

 Tan510

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 #22 : 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.

 

Possible Answers:

Correct answer:

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: 

Tan174

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 #23 : 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.

Possible Answers:

Correct answer:

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:

 Tan43

 

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 .

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