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Tan 62 Degrees

The value of tan 62 degrees is 1.8807264. . .. Tan 62 degrees in radians is written as tan (62° × π/180°), i.e., tan (31π/90) or tan (1.082104. . .). In this article, we will discuss the methods to find the value of tan 62 degrees with examples.

Tan 62° in decimal: 1.8807264. . .
Tan (-62 degrees): -1.8807264. . .
Tan 62° in radians: tan (31π/90) or tan (1.0821041 . . .)

What is the Value of Tan 62 Degrees?

The value of tan 62 degrees in decimal is 1.880726465. . .. Tan 62 degrees can also be expressed using the equivalent of the given angle (62 degrees) in radians (1.08210 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 62 degrees = 62° × (π/180°) rad = 31π/90 or 1.0821 . . .
∴ tan 62° = tan(1.0821) = 1.8807264. . .

Explanation:

For tan 62 degrees, the angle 62° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 62° value = 1.8807264. . .
Since the tangent function is a periodic function, we can represent tan 62° as, tan 62 degrees = tan(62° + n × 180°), n ∈ Z.
⇒ tan 62° = tan 242° = tan 422°, and so on.
Note: Since, tangent is an odd function, the value of tan(-62°) = -tan(62°).

Methods to Find Value of Tan 62 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 62° is given as 1.88072. . .. We can find the value of tan 62 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 62° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 62 degrees as:

sin(62°)/cos(62°)
± sin 62°/√(1 - sin²(62°))
± √(1 - cos²(62°))/cos 62°
± 1/√(cosec²(62°) - 1)
± √(sec²(62°) - 1)
1/cot 62°

Note: Since 62° lies in the 1st Quadrant, the final value of tan 62° will be positive.

We can use trigonometric identities to represent tan 62° as,

cot(90° - 62°) = cot 28°
-cot(90° + 62°) = -cot 152°
-tan (180° - 62°) = -tan 118°

Tan 62 Degrees Using Unit Circle

To find the value of tan 62 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 62° angle with the positive x-axis.
The tan of 62 degrees equals the y-coordinate(0.8829) divided by x-coordinate(0.4695) of the point of intersection (0.4695, 0.8829) of unit circle and r.

Hence the value of tan 62° = y/x = 1.8807 (approx).

☛ Also Check:

Examples Using Tan 62 Degrees

Example 1: Using the value of tan 62°, solve: (sec²(62°) - 1).

Solution:
We know, (sec²(62°) - 1) = (tan²(62°)) = 3.5371
⇒ (sec²(62°) - 1) = 3.5371
Example 2: Find the value of 2 tan 31°/(1 - tan²(31°)). [Hint: Use tan 62° = 1.8807]

Solution:

Using the tan 2a formula,
2 tan 31°/(1 - tan²(31°)) = tan(2 × 31°) = tan 62°
∵ tan 62° = 1.8807
⇒ 2 tan 31°/(1 - tan²(31°)) = 1.8807
Example 3: Find the value of 4 tan(62°)/10 tan(118°).

Solution:

Using trigonometric identities, we know, tan(62°) = -tan(180° - 62°) = -tan 118°.
⇒ tan(62°) = -tan(118°)
⇒ Value of 4 tan(62°)/10 tan(118°) = -4/10 = -2/5

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FAQs on Tan 62 Degrees

What is Tan 62 Degrees?

Tan 62 degrees is the value of tangent trigonometric function for an angle equal to 62 degrees. The value of tan 62° is 1.8807 (approx).

How to Find the Value of Tan 62 Degrees?

The value of tan 62 degrees can be calculated by constructing an angle of 62° with the x-axis, and then finding the coordinates of the corresponding point (0.4695, 0.8829) on the unit circle. The value of tan 62° is equal to the y-coordinate(0.8829) divided by the x-coordinate (0.4695). ∴ tan 62° = 1.8807

What is the Value of Tan 62 Degrees in Terms of Cot 62°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 62° as 1/cot(62°). The value of cot 62° is equal to 0.53170.

What is the Value of Tan 62° in Terms of Cosec 62°?

Since the tangent function can be represented using the cosecant function, we can write tan 62° as 1/√(cosec²(62°) - 1). The value of cosec 62° is equal to 1.13257.

How to Find Tan 62° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 62° can be given in terms of other trigonometric functions as:

sin(62°)/cos(62°)
± sin 62°/√(1 - sin²(62°))
± √(1 - cos²(62°))/cos 62°
± 1/√(cosec²(62°) - 1)
± √(sec²(62°) - 1)
1/cot 62°

☛ Also check: trigonometric table

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