Tan 33 Degrees

The value of tan 33 degrees is 0.6494075. . .. Tan 33 degrees in radians is written as tan (33° × π/180°), i.e., tan (11π/60) or tan (0.575958. . .). In this article, we will discuss the methods to find the value of tan 33 degrees with examples.

• Tan 33° in decimal: 0.6494075. . .
• Tan (-33 degrees): -0.6494075. . .
• Tan 33° in radians: tan (11π/60) or tan (0.5759586 . . .)

What is the Value of Tan 33 Degrees?

The value of tan 33 degrees in decimal is 0.649407593. . .. Tan 33 degrees can also be expressed using the equivalent of the given angle (33 degrees) in radians (0.57595 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 33 degrees = 33° × (π/180°) rad = 11π/60 or 0.5759 . . .
∴ tan 33° = tan(0.5759) = 0.6494075. . .

Explanation:

For tan 33 degrees, the angle 33° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 33° value = 0.6494075. . .
Since the tangent function is a periodic function, we can represent tan 33° as, tan 33 degrees = tan(33° + n × 180°), n ∈ Z.
⇒ tan 33° = tan 213° = tan 393°, and so on.
Note: Since, tangent is an odd function, the value of tan(-33°) = -tan(33°).

Methods to Find Value of Tan 33 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 33° is given as 0.64940. . .. We can find the value of tan 33 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 33° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 33 degrees as:

• sin(33°)/cos(33°)
• ± sin 33°/√(1 - sin²(33°))
• ± √(1 - cos²(33°))/cos 33°
• ± 1/√(cosec²(33°) - 1)
• ± √(sec²(33°) - 1)
• 1/cot 33°

Note: Since 33° lies in the 1st Quadrant, the final value of tan 33° will be positive.

We can use trigonometric identities to represent tan 33° as,

• cot(90° - 33°) = cot 57°
• -cot(90° + 33°) = -cot 123°
• -tan (180° - 33°) = -tan 147°

Tan 33 Degrees Using Unit Circle

To find the value of tan 33 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 33° angle with the positive x-axis.
• The tan of 33 degrees equals the y-coordinate(0.5446) divided by x-coordinate(0.8387) of the point of intersection (0.8387, 0.5446) of unit circle and r.

Hence the value of tan 33° = y/x = 0.6494 (approx).

☛ Also Check:

• tan 60 degrees
• tan 120 degrees
• tan 3 degrees
• tan 6 degrees
• tan 17 degrees
• tan 67 degrees

FAQs on Tan 33 Degrees

What is Tan 33 Degrees?

Tan 33 degrees is the value of tangent trigonometric function for an angle equal to 33 degrees. The value of tan 33° is 0.6494 (approx).

What is the Value of Tan 33 Degrees in Terms of Cos 33°?

We know, using trig identities, we can write tan 33° as √(1 - cos²(33°))/cos 33°. Here, the value of cos 33° is equal to 0.838670.

How to Find the Value of Tan 33 Degrees?

The value of tan 33 degrees can be calculated by constructing an angle of 33° with the x-axis, and then finding the coordinates of the corresponding point (0.8387, 0.5446) on the unit circle. The value of tan 33° is equal to the y-coordinate(0.5446) divided by the x-coordinate (0.8387). ∴ tan 33° = 0.6494

What is the Exact Value of tan 33 Degrees?

The exact value of tan 33 degrees can be given accurately up to 8 decimal places as 0.64940759.

How to Find Tan 33° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 33° can be given in terms of other trigonometric functions as:

• sin(33°)/cos(33°)
• ± sin 33°/√(1 - sin²(33°))
• ± √(1 - cos²(33°))/cos 33°
• ± 1/√(cosec²(33°) - 1)
• ± √(sec²(33°) - 1)
• 1/cot 33°

☛ Also check: trigonometric table