Understanding Tangent and Cotangent

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In summary, the conversation discussed the concepts of tangent and cotangent and their relationship to points on the unit circle. It also covered the calculation of y/x and the value of cotangent when cos(θ) is equal to zero. The conversation also mentioned the use of the unit circle when taking roots.
  • #1
Tyrion101
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I believe I understand both, for instance tangent is equal to y/x and so when you have something like root3/3 it would be equal to the points (root3/2 (x coordinate), and 1/2(y coordinate.) For Cotangent equal to zero, would be (0,1) and (0, -1) am I off base here? I think also that Cot is equal to x/y.
 
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  • #2
Tyrion101 said:
I believe I understand both, for instance tangent is equal to y/x and so when you have something like root3/3 it would be equal to the points (root3/2 (x coordinate), and 1/2(y coordinate.)

You can check your calculations here.

tan θ = y / x

If x = (√3) / 2 and y = 1 / 2, then what is y / x = ?

For Cotangent equal to zero, would be (0,1) and (0, -1) am I off base here? I think also that Cot is equal to x/y.

By definition, cot (θ) = 1 / tan (θ) = cos (θ) / sin (θ)

In order for cot (θ) = 0, this implies that cos (θ) = 0

For which values of θ does cos (θ) = 0? (Hint: check using the unit circle.)
 
  • #3
When you take a root, you want both positive and negative answers on the unit circle yes?
 
  • #4
Tyrion101 said:
When you take a root, you want both positive and negative answers on the unit circle yes?
That's irrelevant in this case.

Your specific example involved x = (√3) / 2 and y = 1 / 2.

If you do the arithmetic to calculate y / x, what number do you get?
 

FAQ: Understanding Tangent and Cotangent

What is a tangent and cotangent?

A tangent is a trigonometric function that describes the ratio of the opposite side of a right triangle to the adjacent side. It is often used to calculate angles and sides of a triangle. Cotangent, on the other hand, is the inverse of tangent and describes the ratio of the adjacent side to the opposite side.

How do you calculate tangent and cotangent?

Tangent and cotangent can be calculated using a scientific calculator or by using trigonometric tables. The formula for tangent is tangent = opposite/adjacent, while the formula for cotangent is cotangent = adjacent/opposite.

What is the relationship between tangent and cotangent?

Tangent and cotangent are inversely related. This means that if the tangent of an angle is known, the cotangent of the same angle can be found by taking the reciprocal of the tangent. Similarly, if the cotangent of an angle is known, the tangent of the same angle can be found by taking the reciprocal of the cotangent.

What are some real-life applications of tangent and cotangent?

Tangent and cotangent are used in a variety of fields, including engineering, physics, and astronomy. They are particularly useful in calculating angles and distances in right triangles. For example, in construction, they can be used to determine the height of a building or the slope of a roof.

What are some common mistakes when working with tangent and cotangent?

One common mistake is mixing up tangent and cotangent. It is important to remember that they are inverse functions and have different formulas. Another mistake is forgetting to check the mode on a calculator, which can result in incorrect calculations. Additionally, forgetting to convert angles to the appropriate unit (degrees or radians) can also lead to errors when working with tangent and cotangent.

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