Question

Find the value of tan 78° 27' ​

Answer 1

Step-by-step explanation:

Tan 78°

Welcome to tan 78°, our post aboutthe tangent of 78 degrees.

For the tangent of 78 degrees we use the abbreviation tan for the trigonometric function together with the degree symbol °, and write it as tan 78°.

If you have been looking for what is tan 78°, or if you have been wondering about tan 78 degrees in radians, then you are right here, too.

In this post you can find the tan 78° value, along with identities.

Read on to learn all about the tan of 78°.

Tan 78 Degrees

If you want to know what is tan 78 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 78°:

tan78° = 4.70463

tan 78° = 4.70463

tan 78 degrees = 4.70463



The tan of 78 degrees is 4.70463, the same as tan of 78 degrees in radians. To obtain 78 degrees in radian multiply 78° by π / 180° = 13/30 π. Tan 78degrees = tan (13/30 × π).

Our results of tan78° have been rounded to five decimal places. If you want tangent 78° with higher accuracy, then use the calculator below; our tool displays ten decimal places.

To calculate tan 78 degrees insert the angle 78 in the field labelled °, but if you want to calculate tan 78 in radians, then you have to press the swap unit button first.

Calculate tan [degrees]

        ° : 

Swap Units

value :

A Really Cool Tangent Calculator and Useful Information! Please ReTweet.CLICK TO TWEETBesides tan78°, similar trigonometric calculations on our site include, but are not limited, to:

Tan 4.34

Tg 5.74

Tan 0.91

The identities of tangent 78° are as follows:

tan78°

= cot (90°-78°) = cot 12°

-tan78°

= tan (-78°) = -tan 78°

= cot (90°+78°) = cot 168°

= tan (180°-78°) = tan 102°

Note that tan78° is periodic: tan (78° + n × 180°) = tan 78 degrees, n∈Z.

There are more formulas for the double angle (2 × 78°), half angle ((78/2)°) as well as the sum, difference and products of two angles such as 78° and β.

You can locate all of them in the respective article found in the header menu. To find everything about tan -78° click the link. And here is all about cot 78°, including, for instance, a converter.

In terms of the other five trigonometric functions, tan of 78° =

±sin⁡78∘1–sin2⁡78∘

±1–cos2⁡78∘cos⁡78∘

±sec2⁡78∘−1

±1csc2⁡78∘–1

1cot⁡78∘

As the cotangent function is the reciprocal of the tangent function, 1 / cot 78° = tan78°.

In the next part of this article we discuss the trigonometric significance of tan78°, and there you can also learn what the search calculations form in the sidebar is used for.

What is tan 78°?

In a triangle which has one angle of 90 degrees, the tangent of the angle of 78° is the ratio of the length of the opposite side o to the length of the adjacent side a: tan 78° = o/a.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, 78 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 78°, x = cos 78° and tan 78° = sin 78°/cos 78°.

Bringing together the triangle definition and the unit circle definition of tangent 78 degrees, a = x, o = y and h = r = 1. It follows that y/x=oppositeadjacent=tan⁡78∘.

Note that you can locate many terms including the tangent78° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of tan78°.

Along the same lines, using the aforementioned form, can you look up terms such as tan 78° value, tan 78, tan78° value and what is the tan of 78 degrees, just to name a few.

Given the periodicity of tangent of 78°, to determine the tangent of an angle > 180°, e.g. 798°, calculate tan 798° as tan (798 Mod 180)° = tangent of 78°, or look it up with