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Other Trigonometric Functions: Cotangent, Secant & Cosecant

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  • 0:01 Trigonometric Functions
  • 1:14 Cotangent
  • 1:51 Secant
  • 2:17 Cosecant
  • 3:04 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will understand how the trigonometric functions cotangent, secant, and cosecant are related to the sine, cosine, and tangent functions.

Trigonometric Functions

Trigonometric functions, functions of angles, are common in math and in the real world. The sound coming out of your computer speakers, for example, is produced by the aid of trigonometric functions, as the sound waves coming out of the speakers are approximated by sine waves. At this point, you are familiar with the sine, cosine, and tangent functions. These are your basic three trigonometric functions. All other trigonometric functions are based on these three functions, as you will see.

Do you remember what the sine, cosine, and tangent functions are? Recall your right triangle with its three sides of hypotenuse, opposite, and adjacent. Looking at this right triangle, do you recall how we can define our three basic functions?

Three basic trigonometric functions
right triangle and trig functions

Yes, the sine is defined as opposite/hypotenuse; the cosine is defined as adjacent/hypotenuse; the tangent is defined as opposite/adjacent - remember SOH - CAH - TOA for these. Now that we've reviewed these three trigonometric functions, or trig functions for short, let's go over the three other trigonometric functions of cotangent, secant, and cosecant.

Cotangent

First, we have the cotangent function. It is defined as the reciprocal of the tangent function. In math, we write this as cot(theta) = 1/tan(theta). All of our trigonometric functions are shortened to three letters when written out as functions. Now, because cotangent is the reciprocal of the tangent function, we can also define it as the flipped version of the tangent. If the tangent is opposite/adjacent, then our cotangent is the reciprocal of that, or adjacent/opposite. We can write all of this information like this:

other trig functions

Secant

Next, we have the secant function. We define the secant function as the reciprocal of the cosine function. The three letter short version of secant is sec. Do you remember how cosine is defined? Cosine is defined as adjacent/hypotenuse. If the secant is the reciprocal of this, then we can flip this definition to get our other definition of secant as hypotenuse/adjacent:

other trig functions

Cosecant

Finally, we have cosecant. This function is the reciprocal of the sine function. The short version of this function is csc. Because this is the reciprocal of the sine function, and the sine function is defined as opposite/hypotenuse, we can alternately define our cosecant function as hypotenuse/opposite:

other trig functions

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