How to find positive tangent - ACT Math

The cotangent of the angle of a triangle is the adjacent side over the opposite side. The answer is

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 third quadrant of the Cartesian plane. It would look like:

So, the tangent of an angle is:

or, for your data, , or . Since is in the third quadrant, your value must be positive, as the tangent function is positive in this quadrant.

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 third 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 . Since is in the third quadrant, your value must be positive, as the tangent function is positive in that quadrant.

Based on our information, we can draw this little triangle:

Since we know that the tangent of an angle is , we can say:

This can be solved using your calculator:

or

Now, to solve for , use the Pythagorean Theorem, , where and are the legs of a triangle and is the triangle's hypotenuse. Here, , so we can substitute that in and rearrange the equation to solve for :

Substituting in the known values:

, or approximately . Rounding, this is .

The cotangent of the angle of a triangle is the adjacent side over the opposite side. The answer is

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 third quadrant of the Cartesian plane. It would look like:

So, the tangent of an angle is:

or, for your data, , or . Since is in the third quadrant, your value must be positive, as the tangent function is positive in this quadrant.

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 third 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 . Since is in the third quadrant, your value must be positive, as the tangent function is positive in that quadrant.

Based on our information, we can draw this little triangle:

Since we know that the tangent of an angle is , we can say:

This can be solved using your calculator:

or

Now, to solve for , use the Pythagorean Theorem, , where and are the legs of a triangle and is the triangle's hypotenuse. Here, , so we can substitute that in and rearrange the equation to solve for :

Substituting in the known values:

, or approximately . Rounding, this is .

The cotangent of the angle of a triangle is the adjacent side over the opposite side. The answer is

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 third quadrant of the Cartesian plane. It would look like:

So, the tangent of an angle is:

or, for your data, , or . Since is in the third quadrant, your value must be positive, as the tangent function is positive in this quadrant.

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 third 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 . Since is in the third quadrant, your value must be positive, as the tangent function is positive in that quadrant.

Based on our information, we can draw this little triangle:

Since we know that the tangent of an angle is , we can say:

This can be solved using your calculator:

or

Now, to solve for , use the Pythagorean Theorem, , where and are the legs of a triangle and is the triangle's hypotenuse. Here, , so we can substitute that in and rearrange the equation to solve for :

Substituting in the known values:

, or approximately . Rounding, this is .

The cotangent of the angle of a triangle is the adjacent side over the opposite side. The answer is

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 third quadrant of the Cartesian plane. It would look like:

So, the tangent of an angle is:

or, for your data, , or . Since is in the third quadrant, your value must be positive, as the tangent function is positive in this quadrant.

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 third 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 . Since is in the third quadrant, your value must be positive, as the tangent function is positive in that quadrant.

Based on our information, we can draw this little triangle:

Since we know that the tangent of an angle is , we can say:

This can be solved using your calculator:

or

Now, to solve for , use the Pythagorean Theorem, , where and are the legs of a triangle and is the triangle's hypotenuse. Here, , so we can substitute that in and rearrange the equation to solve for :

Substituting in the known values:

, or approximately . Rounding, this is .

The cotangent of the angle of a triangle is the adjacent side over the opposite side. The answer is

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 third quadrant of the Cartesian plane. It would look like:

So, the tangent of an angle is:

or, for your data, , or . Since is in the third quadrant, your value must be positive, as the tangent function is positive in this quadrant.

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 third 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 . Since is in the third quadrant, your value must be positive, as the tangent function is positive in that quadrant.

Based on our information, we can draw this little triangle:

Since we know that the tangent of an angle is , we can say:

This can be solved using your calculator:

or

Now, to solve for , use the Pythagorean Theorem, , where and are the legs of a triangle and is the triangle's hypotenuse. Here, , so we can substitute that in and rearrange the equation to solve for :

Substituting in the known values:

, or approximately . Rounding, this is .