What are the cotangent, secant, and cosecant values on the Unit Circle?

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What are the cotangent, secant, and cosecant values on the Unit Circle?

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Answer 1 · 2015-04-21T15:05:24

You can find the value of $cot x$ on the trig unit circle with origin $O$ .
Suppose $M$ is the extremity of the variable arc $AM = x$ , and $B$ is the top point of the circle. The line $AM$ cut the horizontal tangent axis $Bz$ at point $V$ . The segment $BV$ is the measure of $cot x$ .
The trig unit circle only shows the 4 values of the 4 trig functions ( $cos x$ , $sin x$ , $tan x$ , $cot x$ ) of the arc $AM = x$ . The unit circle doesn't show the values of $sec x$ and $csc x$ .

Answer 2 · 2015-04-21T19:21:41

If $t$ (or $theta$ ) is associated with the point $(x,y)$ on the unit circle, then

$sint=y$ $color(white)"sssssssssssssssssss"$ $csct = 1/y$ (for $y!=0$ )

$cost=x$ $color(white)"sssssssssssssssssss"$ $sect = 1/x$ (for $x!=0$ )

$tant=y/x$ (for $x!=0$ ) $color(white)"sssssss"$ $cott = x/y$ (for $y!=0$ )

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What are the cotangent, secant, and cosecant values on the Unit Circle?

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