Tan 75° – Tan75° Value – What is the tan of 75 degrees? (2024)

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Welcome to tan 75°, our post aboutthe tangent of 75 degrees.

For the tangent of 75 degrees we use the abbreviation tan for the trigonometric function together with the degree symbol °, and write it as tan 75°.

If you have been looking for what is tan 75°, or if you have been wondering about tan 75 degrees in radians, then you are right here, too.

In this post you can find the tan 75° value, along with identities.

Read on to learn all about the tan of 75°.

Tan 75 Degrees

If you want to know what is tan 75 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 75°:

tan75° = 2+√3
tan 75° = 2+√3
tan 75 degrees = 2+√3

Tan 75° – Tan75° Value – What is the tan of 75 degrees? (1)

The tan of 75 degrees is 2+√3, the same as tan of 75 degrees in radians. To obtain 75 degrees in radian multiply 75° by $\pi$ / 180° = 5/12 $\pi$. Tan 75degrees = tan (5/12 × $\pi)$.

Our results of tan75° have been rounded to five decimal places. If you want tangent 75° with higher accuracy, then use the calculator below; our tool displays ten decimal places.

To calculate tan 75 degrees insert the angle 75 in the field labelled °, but if you want to calculate tan 75 in radians, then you have to press the swap unit button first.

Calculate tan [degrees]

A Really Cool Tangent Calculator and Useful Information! Please ReTweet. Click To TweetBesides tan75°, similar trigonometric calculations on our site include, but are not limited, to:

  • Tg 4.02
  • Tg 1.24
  • Tan 341°

The identities of tangent 75° are as follows:

tan75°
= cot (90°-75°) = cot 15°

-tan75°
= tan (-75°) = -tan 75°
= cot (90°+75°) = cot 165°
= tan (180°-75°) = tan 105°

Note that tan75° is periodic: tan (75° + n × 180°) = tan 75 degrees, n$\hspace{5px} \in \hspace{5px} \mathbb{Z}$.

There are more formulas for the double angle (2 × 75°), half angle ((75/2)°) as well as the sum, difference and products of two angles such as 75° and β.

You can locate all of them in the respective article found in the header menu. To find everything about tan -75° click the link. And here is all about cot 75°, including, for instance, a converter.

In terms of the other five trigonometric functions, tan of 75° =

  • $\pm\frac{\sin 75^\circ}{\sqrt{1 – \sin^{2} 75^\circ}}$
  • $\pm\frac{\sqrt{1 – \cos^{2} 75^\circ}}{\cos 75^\circ}$
  • $\pm \sqrt{\sec^{2} 75^\circ -1}$
  • $\pm\frac{1}{\sqrt{\csc^2 75^\circ – 1}}$
  • $\frac{1}{\cot 75^\circ}$

As the cotangent function is the reciprocal of the tangent function, 1 / cot 75° = tan75°.

In the next part of this article we discuss the trigonometric significance of tan75°, and there you can also learn what the search calculations form in the sidebar is used for.

What is tan 75°?

In a triangle which has one angle of 90 degrees, the tangent of the angle of 75° is the ratio of the length of the opposite side o to the length of the adjacent side a: tan 75° = o/a.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, 75 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 75°, x = cos 75° and tan 75° = sin 75°/cos 75°.

Bringing together the triangle definition and the unit circle definition of tangent 75 degrees, a = x, o = y and h = r = 1. It follows that $y/x\hspace{5px} =\hspace{5px}\frac{opposite}{adjacent}\hspace{5px}=\hspace{5px}\tan 75^\circ$.

Note that you can locate many terms including the tangent75° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of tan75°.

Along the same lines, using the aforementioned form, can you look up terms such as tan 75° value, tan 75, tan75° value and what is the tan of 75 degrees, just to name a few.

Given the periodicity of tangent of 75°, to determine the tangent of an angle > 180°, e.g. 795°, calculate tan 795° as tan (795 Mod 180)° = tangent of 75°, or look it up with our form.

Conclusion

Tan 75° – Tan75° Value – What is the tan of 75 degrees? (2)The frequently asked questions in the context include what is tan 75 degrees and what is the tan of 75 degrees for example; reading our content they are no-brainers.

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– Article written by Mark, last updated on February 26th, 2017

Tan 75° – Tan75° Value – What is the tan of 75 degrees? (2024)

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