Table of Contents
Welcome to ctg pi/2, our post aboutthe cotangent of pi/2.
For the cotangent of pi/2 we use the abbreviation ctg for the trigonometric function and write it as ctg pi/2.
If you have been looking for what is ctg pi/2, or if you have been wondering about ctg pi/2 radians in degrees, then you are right here, too.
In this post you can find the ctg pi/2 value, along with identities.
Read on to learn all about the ctg of pi/2.
Ctg Pi/2 Radians
If you want to know what is ctg pi/2 radians in terms of trigonometry, then navigate straight to the explanations in the next paragraph; what’s ahead in this section is the value of ctg pi/2:
ctg pi/2 = 0
ctg pi/2 radians = 0
The ctg of pi/2 radians is 0, the same as ctg of pi/2 radians in degrees. To change pi/2 radians to degrees multiply pi/2 by 180° / $\pi$ = 90°. Ctg pi/2 = ctg 90 degrees.
Our results of ctgpi/2 have been rounded to five decimal places. If you want cotangent pi/2 with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate ctg pi/2 radians insert the angle pi/2 in decimal notation, but if you want to calculate ctg pi/2 in degrees, then you have to press the swap unit button first.
Calculate ctg [radians]
The identities of cotangent pi/2 are as follows:
= tg (pi/2 – pi/2) = tg 0
-ctgpi/2
= ctg (-pi/2) = -ctg pi/2
= tg (pi/2 + pi/2) = tg pi
= ctg (pi – pi/2) = ctg 1/2 pi
There are more formulas for the double angle (2 × pi/2), half angle ((pi/2/2)) as well as the sum, difference and products of two angles such as pi/2 and β.
You can locate all of them in the respective article found in the header menu. To find everything about ctg -pi/2 click the link. And here is all about tg pi/2, including, for instance, a converter.
In terms of the other five trigonometric functions, ctg of pi/2 =
- $\pm\frac{\sqrt{1 – \sin^{2} \pi/2}}{\sin \pi/2}$
- $\pm\frac{\cos \pi/2}{\sqrt{1 – \cos^{2} \pi/2}}$
- $\pm \sqrt{\csc^{2} (\pi/2) – 1}$
- $\pm\frac{1}{\sqrt{\csc^2 (\pi/2) – 1}}$
- $\frac{1}{tg\hspace{3px}\pi/2}$
As the tangent function is the reciprocal of the cotangent function, 1 / tg pi/2 = ctgpi/2.
In the next part of this article we discuss the trigonometric significance of ctgpi/2, and there you can also learn what the search calculations form in the sidebar is used for.
What is ctg Pi/2?
In a triangle which has one angle of pi/2, the cotangent of the angle of pi/2 is the ratio of the length of the adjacent side a to the length of the opposite side o: ctg pi/2 = a/o.
In a circle with the radius r, the horizontal axis x, and the vertical axis y, pi/2 is the angle formed by the two sides x and r; r moving counterclockwise is the positive angle.
Applying the unit-circle definition found on our homepage, assumed r = 1, in the intersection of the point (x,y) and the circle, y = sin pi/2, x = cos pi/2 and ctg pi/2 = cos pi/2/sin pi/2.
Bringing together the triangle definition and the unit circle definition of cotangent pi/2, a = x, o = y and h = r = 1. It follows that $x/y\hspace{5px} =\hspace{5px}\frac{adjacent}{opposite}\hspace{5px}=\hspace{5px}ctg\hspace{5px} \pi/2$.
Note that you can locate many terms including the cotangentpi/2 value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of ctgpi/2.
Along the same lines, using the aforementioned form, can you look up terms such as ctg pi/2 value, ctg pi/2, ctgpi/2 value and what is the ctg of pi/2 radians, just to name a few.
Given the periodicity of cotangent of pi/2, to determine the cotangent of an angle > pi, e.g. 9/2 pi, calculate ctg 9/2 pi as ctg (9/2 pi mod pi) = cotangent of pi/2, or use our form.
Conclusion
The frequently asked questions in the context include what is ctg pi/2 radians and what is the ctg of pi/2 radians for example; reading our content they are no-brainers.
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– Article written by Mark, last updated on February 26th, 2017