Tan 63 Degrees

The value of tan 63 degrees is 1.9626105. . .. Tan 63 degrees in radians is written as tan (63° × π/180°), i.e., tan (7π/20) or tan (1.099557. . .). In this article, we will discuss the methods to find the value of tan 63 degrees with examples.

• Tan 63° in decimal: 1.9626105. . .
• Tan (-63 degrees): -1.9626105. . .
• Tan 63° in radians: tan (7π/20) or tan (1.0995574 . . .)

What is the Value of Tan 63 Degrees?

The value of tan 63 degrees in decimal is 1.962610505. . .. Tan 63 degrees can also be expressed using the equivalent of the given angle (63 degrees) in radians (1.09955 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 63 degrees = 63° × (π/180°) rad = 7π/20 or 1.0995 . . .
∴ tan 63° = tan(1.0995) = 1.9626105. . .

Explanation:

For tan 63 degrees, the angle 63° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 63° value = 1.9626105. . .
Since the tangent function is a periodic function, we can represent tan 63° as, tan 63 degrees = tan(63° + n × 180°), n ∈ Z.
⇒ tan 63° = tan 243° = tan 423°, and so on.
Note: Since, tangent is an odd function, the value of tan(-63°) = -tan(63°).

Methods to Find Value of Tan 63 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 63° is given as 1.96261. . .. We can find the value of tan 63 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 63° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 63 degrees as:

• sin(63°)/cos(63°)
• ± sin 63°/√(1 - sin²(63°))
• ± √(1 - cos²(63°))/cos 63°
• ± 1/√(cosec²(63°) - 1)
• ± √(sec²(63°) - 1)
• 1/cot 63°

Note: Since 63° lies in the 1st Quadrant, the final value of tan 63° will be positive.

We can use trigonometric identities to represent tan 63° as,

• cot(90° - 63°) = cot 27°
• -cot(90° + 63°) = -cot 153°
• -tan (180° - 63°) = -tan 117°

Tan 63 Degrees Using Unit Circle

To find the value of tan 63 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 63° angle with the positive x-axis.
• The tan of 63 degrees equals the y-coordinate(0.891) divided by x-coordinate(0.454) of the point of intersection (0.454, 0.891) of unit circle and r.

Hence the value of tan 63° = y/x = 1.9626 (approx).

☛ Also Check:

• tan 120 degrees
• tan 75 degrees
• tan 30 degrees
• tan 38 degrees
• tan 58 degrees
• tan 33 degrees

FAQs on Tan 63 Degrees

What is Tan 63 Degrees?

Tan 63 degrees is the value of tangent trigonometric function for an angle equal to 63 degrees. The value of tan 63° is 1.9626 (approx).

What is the Value of Tan 63 Degrees in Terms of Cot 63°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 63° as 1/cot(63°). The value of cot 63° is equal to 0.50952.

How to Find the Value of Tan 63 Degrees?

The value of tan 63 degrees can be calculated by constructing an angle of 63° with the x-axis, and then finding the coordinates of the corresponding point (0.454, 0.891) on the unit circle. The value of tan 63° is equal to the y-coordinate(0.891) divided by the x-coordinate (0.454). ∴ tan 63° = 1.9626

What is the Exact Value of tan 63 Degrees?

The exact value of tan 63 degrees can be given accurately up to 8 decimal places as 1.96261050.

How to Find Tan 63° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 63° can be given in terms of other trigonometric functions as:

• sin(63°)/cos(63°)
• ± sin 63°/√(1 - sin²(63°))
• ± √(1 - cos²(63°))/cos 63°
• ± 1/√(cosec²(63°) - 1)
• ± √(sec²(63°) - 1)
• 1/cot 63°

☛ Also check: trigonometric table