A day full of math games & activities. Find one near you.

Tan 89 Degrees

The value of tan 89 degrees is 57.2899616. . .. Tan 89 degrees in radians is written as tan (89° × π/180°), i.e., tan (1.553343. . .). In this article, we will discuss the methods to find the value of tan 89 degrees with examples.

Tan 89° in decimal: 57.2899616. . .
Tan (-89 degrees): -57.2899616. . .
Tan 89° in radians: tan (1.5533430 . . .)

What is the Value of Tan 89 Degrees?

The value of tan 89 degrees in decimal is 57.289961630. . .. Tan 89 degrees can also be expressed using the equivalent of the given angle (89 degrees) in radians (1.55334 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 89 degrees = 89° × (π/180°) rad = 1.5533 . . .
∴ tan 89° = tan(1.5533) = 57.2899616. . .

Explanation:

For tan 89 degrees, the angle 89° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 89° value = 57.2899616. . .
Since the tangent function is a periodic function, we can represent tan 89° as, tan 89 degrees = tan(89° + n × 180°), n ∈ Z.
⇒ tan 89° = tan 269° = tan 449°, and so on.
Note: Since, tangent is an odd function, the value of tan(-89°) = -tan(89°).

Methods to Find Value of Tan 89 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 89° is given as 57.28996. . .. We can find the value of tan 89 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 89° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 89 degrees as:

sin(89°)/cos(89°)
± sin 89°/√(1 - sin²(89°))
± √(1 - cos²(89°))/cos 89°
± 1/√(cosec²(89°) - 1)
± √(sec²(89°) - 1)
1/cot 89°

Note: Since 89° lies in the 1st Quadrant, the final value of tan 89° will be positive.

We can use trigonometric identities to represent tan 89° as,

cot(90° - 89°) = cot 1°
-cot(90° + 89°) = -cot 179°
-tan (180° - 89°) = -tan 91°

Tan 89 Degrees Using Unit Circle

To find the value of tan 89 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 89° angle with the positive x-axis.
The tan of 89 degrees equals the y-coordinate(0.9998) divided by x-coordinate(0.0175) of the point of intersection (0.0175, 0.9998) of unit circle and r.

Hence the value of tan 89° = y/x = 57.29 (approx).

☛ Also Check:

Examples Using Tan 89 Degrees

Example 1: Find the value of 3 tan(89°)/5 tan(91°).

Solution:

Using trigonometric identities, we know, tan(89°) = -tan(180° - 89°) = -tan 91°.
⇒ tan(89°) = -tan(91°)
⇒ Value of 3 tan(89°)/5 tan(91°) = -3/5
Example 2: Using the value of tan 89°, solve: (sec²(89°) - 1).

Solution:
We know, (sec²(89°) - 1) = (tan²(89°)) = 3282.1397
⇒ (sec²(89°) - 1) = 3282.1397
Example 3: Find the value of (2 sin (44.5°) cos (44.5°) sec (89°)). [Hint: Use tan 89° = 57.29]

Solution:

Using sin 2a formula,
2 sin (44.5°) cos (44.5°) = sin (2 × 44.5°) = sin 89°
⇒ 2 sin (44.5°) cos (44.5°) sec(89°) = sin 89° sec 89°
= sin 89°/cos 89° = tan 89°
⇒ (2 sin (44.5°) cos (44.5°) sec(89°)) = 57.29

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Tan 89 Degrees

What is Tan 89 Degrees?

Tan 89 degrees is the value of tangent trigonometric function for an angle equal to 89 degrees. The value of tan 89° is 57.29 (approx).

What is the Value of Tan 89 Degrees in Terms of Cot 89°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 89° as 1/cot(89°). The value of cot 89° is equal to 0.01745.

How to Find the Value of Tan 89 Degrees?

The value of tan 89 degrees can be calculated by constructing an angle of 89° with the x-axis, and then finding the coordinates of the corresponding point (0.0175, 0.9998) on the unit circle. The value of tan 89° is equal to the y-coordinate(0.9998) divided by the x-coordinate (0.0175). ∴ tan 89° = 57.29

What is the Value of Tan 89° in Terms of Sec 89°?

We can represent the tangent function in terms of the secant function using trig identities, tan 89° can be written as √(sec²(89°) - 1). Here, the value of sec 89° is equal to 57.2986.

How to Find Tan 89° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 89° can be given in terms of other trigonometric functions as:

sin(89°)/cos(89°)
± sin 89°/√(1 - sin²(89°))
± √(1 - cos²(89°))/cos 89°
± 1/√(cosec²(89°) - 1)
± √(sec²(89°) - 1)
1/cot 89°

☛ Also check: trigonometric table

Download FREE Study Materials

Trigonometry

Math worksheets and
visual curriculum