The value of **tan 90 levels is undefined (or, ∞)**. Tan 90 degrees in radians is created as tan (90° × π/180°), i.e., tan (π/2) or tan (1.570796. . .). In this article, us will comment on the methods to discover the worth of tan 90 degrees with examples.

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## What is the worth of Tan 90 Degrees?

The worth of tan 90 levels is undefined(∞). Tan 90 levels can additionally be expressed using the equivalent of the provided angle (90 degrees) in radians (1.57079 . . .)

We know, using level to radian conversion, θ in radians = θ in degrees × (pi/180°)⇒ 90 degrees = 90° × (π/180°) rad = π/2 or 1.5707 . . .∴ tan 90° = tan(1.5707) = undefined(∞)

**Explanation: **

For tan 90 degrees, the edge 90° lies on the hopeful y-axis. Thus, tan 90° worth = undefined(∞)Since the tangent function is a routine function, we deserve to represent tan 90° as, tan 90 degrees = tan(90° + n × 180°), n ∈ Z.⇒ tan 90° = tan 270° = tan 450°, and so on.**Note:** Since, tangent is one odd function, the worth of tan(-90°) = -tan(90°) = undefined.

## Methods to discover Value of Tan 90 Degrees

The value of tan 90° is given as undefined(∞). We can discover the value of tan 90 degrees by:

Using Unit CircleUsing Trigonometric Functions## Tan 90 levels Using Unit Circle

To find the worth of tan 90 levels using the unit circle:

Rotate ‘r’ anticlockwise to form 90° angle v the hopeful x-axis.The tan the 90 degrees equals the y-coordinate(1) divided by x-coordinate(0) that the point of intersection (0, 1) that unit circle and also r.Hence the worth of tan 90° = y/x = undefined(∞)

## Tan 90° in terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 90 degrees as:

sin(90°)/cos(90°)± sin 90°/√(1 - sin²(90°))± √(1 - cos²(90°))/cos 90°± 1/√(cosec²(90°) - 1)± √(sec²(90°) - 1)1/cot 90°We can use trigonometric identities to represent tan 90° as,

cot(90° - 90°) = cot 0°-cot(90° + 90°) = -cot 180°-tan (180° - 90°) = -tan 90°Note: because 90° lies on the hopeful y-axis, the last value that tan 90° will certainly be undefined(∞).

**☛ additionally Check: **

## FAQs on Tan 90 Degrees

### What is Tan 90 Degrees?

Tan 90 degrees is the value of tangent trigonometric duty for one angle same to 90 degrees. ** The value of tan 90° is undefined(∞). **

### How to discover the worth of Tan 90 Degrees?

The worth of tan 90 levels can it is in calculated by building an edge of 90° through the x-axis, and also then recognize the collaborates of the corresponding allude (0, 1) ~ above the unit circle. The worth of tan 90° is same to the y-coordinate(1) separated by the x-coordinate (0). ∴ tan 90° = undefined(∞)

### How to discover Tan 90° in state of other Trigonometric Functions?

Using trigonometry formula, the value of tan 90° have the right to be given in terms of various other trigonometric features as:

sin(90°)/cos(90°)± sin 90°/√(1 - sin²(90°))± √(1 - cos²(90°))/cos 90°± 1/√(cosec²(90°) - 1)± √(sec²(90°) - 1)1/cot 90°☛ likewise check: trigonometry table

### What is the value of Tan 90 levels in terms of Cot 90°?

Since the tangent function is the reciprocal of the cotangent function, we deserve to write tan 90° as 1/cot(90°). The value of cot 90° is same to 0.

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### What is the value of Tan 90° in regards to Cosec 90°?

Since the tangent duty can be stood for using the cosecant function, we deserve to write tan 90° as 1/√(cosec²(90°) - 1). The value of cosec 90° is same to 1.