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.

You are watching: What is the tan of 90

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.

See more: Q: Is 45 A Prime Or Composite Number ? Q: Is 45 A Composite Number

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.