Tan 32 Degrees

The value of tan 32 degrees is 0.6248693. . .. Tan 32 degrees in radians is written as tan (32° × π/180°), i.e., tan (8π/45) or tan (0.558505. . .). In this article, we will discuss the methods to find the value of tan 32 degrees with examples.

• Tan 32° in decimal: 0.6248693. . .
• Tan (-32 degrees): -0.6248693. . .
• Tan 32° in radians: tan (8π/45) or tan (0.5585053 . . .)

What is the Value of Tan 32 Degrees?

The value of tan 32 degrees in decimal is 0.624869351. . .. Tan 32 degrees can also be expressed using the equivalent of the given angle (32 degrees) in radians (0.55850 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 32 degrees = 32° × (π/180°) rad = 8π/45 or 0.5585 . . .
∴ tan 32° = tan(0.5585) = 0.6248693. . .

Explanation:

For tan 32 degrees, the angle 32° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 32° value = 0.6248693. . .
Since the tangent function is a periodic function, we can represent tan 32° as, tan 32 degrees = tan(32° + n × 180°), n ∈ Z.
⇒ tan 32° = tan 212° = tan 392°, and so on.
Note: Since, tangent is an odd function, the value of tan(-32°) = -tan(32°).

Methods to Find Value of Tan 32 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 32° is given as 0.62486. . .. We can find the value of tan 32 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 32° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 32 degrees as:

• sin(32°)/cos(32°)
• ± sin 32°/√(1 - sin²(32°))
• ± √(1 - cos²(32°))/cos 32°
• ± 1/√(cosec²(32°) - 1)
• ± √(sec²(32°) - 1)
• 1/cot 32°

Note: Since 32° lies in the 1st Quadrant, the final value of tan 32° will be positive.

We can use trigonometric identities to represent tan 32° as,

• cot(90° - 32°) = cot 58°
• -cot(90° + 32°) = -cot 122°
• -tan (180° - 32°) = -tan 148°

Tan 32 Degrees Using Unit Circle

To find the value of tan 32 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 32° angle with the positive x-axis.
• The tan of 32 degrees equals the y-coordinate(0.5299) divided by x-coordinate(0.848) of the point of intersection (0.848, 0.5299) of unit circle and r.

Hence the value of tan 32° = y/x = 0.6249 (approx).

☛ Also Check:

• tan 50 degrees
• tan 690 degrees
• tan 60 degrees
• tan 22 degrees
• tan 240 degrees
• tan 73 degrees

FAQs on Tan 32 Degrees

What is Tan 32 Degrees?

Tan 32 degrees is the value of tangent trigonometric function for an angle equal to 32 degrees. The value of tan 32° is 0.6249 (approx).

How to Find Tan 32° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 32° can be given in terms of other trigonometric functions as:

• sin(32°)/cos(32°)
• ± sin 32°/√(1 - sin²(32°))
• ± √(1 - cos²(32°))/cos 32°
• ± 1/√(cosec²(32°) - 1)
• ± √(sec²(32°) - 1)
• 1/cot 32°

☛ Also check: trigonometry table

What is the Value of Tan 32° in Terms of Cosec 32°?

Since the tangent function can be represented using the cosecant function, we can write tan 32° as 1/√(cosec²(32°) - 1). The value of cosec 32° is equal to 1.88707.

How to Find the Value of Tan 32 Degrees?

The value of tan 32 degrees can be calculated by constructing an angle of 32° with the x-axis, and then finding the coordinates of the corresponding point (0.848, 0.5299) on the unit circle. The value of tan 32° is equal to the y-coordinate(0.5299) divided by the x-coordinate (0.848). ∴ tan 32° = 0.6249

What is the Value of Tan 32 Degrees in Terms of Cot 32°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 32° as 1/cot(32°). The value of cot 32° is equal to 1.60033.