Tan 53°


Welcome to tan 53°, our post about the tangent of 53 degrees. For the tangent of 53 degrees we use the abbreviation tan for the trigonometric function together with the degree symbol °, and write it as tan 53°. If you have been looking for what is tan 53°, or if you have been wondering about tan 53 degrees in radians, then you are right here, too. In this post you can find the tan 53° value, along with identities. Read on to learn all about the tan of 53°.

Tan 53 Degrees

If you want to know what is tan 53 degrees in terms of trigonometry, then navigate straight to the explanations in the next paragraph; what’s ahead in this section is the value of tan 53°:


tan53° = 1.32704
tan 53° = 1.32704
tan 53 degrees = 1.32704

The tan of 53 degrees is 1.32704, the same as tan of 53 degrees in radians. To obtain 53 degrees in radian multiply 53° by $\pi$ / 180° = 53/180 $\pi$. Tan 53degrees = tan (53/180 × $\pi)$.

Our results of tan53° have been rounded to five decimal places. If you want tangent 53° with higher accuracy, then use the calculator below; our tool displays ten decimal places.

To calculate tan 53 degrees insert the angle 53 in the field labelled °, but if you want to calculate tan 53 in radians, then you have to press the swap unit button first.

Calculate tan [degrees]

        ° :
value :


Besides tan53°, similar trigonometric calculations on our site include, but are not limited, to:

The identities of tangent 53° are as follows:

tan53°
= cot (90°-53°) = cot 37°

-tan53°
= tan (-53°) = -tan 53°
= cot (90°+53°) = cot 143°
= tan (180°-53°) = tan 127°

Note that tan53° is periodic: tan (53° + n × 180°) = tan 53 degrees, n$\hspace{5px} \varepsilon \hspace{5px} \mathbb{Z}$.

There are more formulas for the double angle (2 × 53°), half angle ((53/2)°) as well as the sum, difference and products of two angles such as 53° and β.

You can locate all of them in the respective article found in the header menu. To find everything about tan -53° click the link. And here is all about cot 53°, including, for instance, a converter.

In terms of the other five trigonometric functions, tan of 53° =

  • $\pm\frac{\sin 53^\circ}{\sqrt{1 – \sin^{2} 53^\circ}}$
  • $\pm\frac{\sqrt{1 – \cos^{2} 53^\circ}}{\cos 53^\circ}$
  • $\pm \sqrt{\sec^{2} 53^\circ -1}$
  • $\pm\frac{1}{\sqrt{\csc^2 53^\circ – 1}}$
  • $\frac{1}{\cot 53^\circ}$

As the cotangent function is the reciprocal of the tangent function, 1 / cot 53° = tan53°.

In the next part of this article we discuss the trigonometric significance of tan53°, and there you can also learn what the search calculations form in the sidebar is used for.

What is tan 53°

In a triangle which has one angle of 90 degrees, the tangent of the angle of 53° is the ratio of the length of the opposite side o to the length of the adjacent side a: tan 53° = o/a.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, 53 degrees 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 53°, x = cos 53° and tan 53° = sin 53°/cos 53°.

Bringing together the triangle definition and the unit circle definition of tangent 53 degrees, a = x, o = y and h = r = 1. It follows that $y/x\hspace{5px} =\hspace{5px}\frac{opposite}{adjacent}\hspace{5px}=\hspace{5px}\tan 53^\circ$.

Note that you can locate many terms including the tangent53° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of tan53°.

Along the same lines, using the aforementioned form, can you look up terms such as tan 53° value, tan 53, tan53° value and what is the tan of 53 degrees, just to name a few.

Given the periodicity of tangent of 53°, to determine the tangent of an angle > 180°, e.g. 773°, calculate tan 773° as tan (773 Mod 180)° = tangent of 53°, or look it up with our form.

The frequently asked questions in the context include what is tan 53 degrees and what is the tan of 53 degrees for example; reading our content they are no-brainers.

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