Tan 34 Degrees

The value of tan 34 degrees is 0.6745085. . .. Tan 34 degrees in radians is written as tan (34° × π/180°), i.e., tan (17π/90) or tan (0.593411. . .). In this article, we will discuss the methods to find the value of tan 34 degrees with examples.

• Tan 34° in decimal: 0.6745085. . .
• Tan (-34 degrees): -0.6745085. . .
• Tan 34° in radians: tan (17π/90) or tan (0.5934119 . . .)

What is the Value of Tan 34 Degrees?

The value of tan 34 degrees in decimal is 0.674508516. . .. Tan 34 degrees can also be expressed using the equivalent of the given angle (34 degrees) in radians (0.59341 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 34 degrees = 34° × (π/180°) rad = 17π/90 or 0.5934 . . .
∴ tan 34° = tan(0.5934) = 0.6745085. . .

Explanation:

For tan 34 degrees, the angle 34° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 34° value = 0.6745085. . .
Since the tangent function is a periodic function, we can represent tan 34° as, tan 34 degrees = tan(34° + n × 180°), n ∈ Z.
⇒ tan 34° = tan 214° = tan 394°, and so on.
Note: Since, tangent is an odd function, the value of tan(-34°) = -tan(34°).

Methods to Find Value of Tan 34 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 34° is given as 0.67450. . .. We can find the value of tan 34 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 34 Degrees Using Unit Circle

To find the value of tan 34 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 34° angle with the positive x-axis.
• The tan of 34 degrees equals the y-coordinate(0.5592) divided by x-coordinate(0.829) of the point of intersection (0.829, 0.5592) of unit circle and r.

Hence the value of tan 34° = y/x = 0.6745 (approx).

Tan 34° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 34 degrees as:

• sin(34°)/cos(34°)
• ± sin 34°/√(1 - sin²(34°))
• ± √(1 - cos²(34°))/cos 34°
• ± 1/√(cosec²(34°) - 1)
• ± √(sec²(34°) - 1)
• 1/cot 34°

Note: Since 34° lies in the 1st Quadrant, the final value of tan 34° will be positive.

We can use trigonometric identities to represent tan 34° as,

• cot(90° - 34°) = cot 56°
• -cot(90° + 34°) = -cot 124°
• -tan (180° - 34°) = -tan 146°

☛ Also Check:

• tan 50 degrees
• tan 180 degrees
• tan 690 degrees
• tan 1290 degrees
• tan 5 degrees
• tan 51 degrees

FAQs on Tan 34 Degrees

What is Tan 34 Degrees?

Tan 34 degrees is the value of tangent trigonometric function for an angle equal to 34 degrees. The value of tan 34° is 0.6745 (approx).

What is the Value of Tan 34° in Terms of Sec 34°?

We can represent the tangent function in terms of the secant function using trig identities, tan 34° can be written as √(sec²(34°) - 1). Here, the value of sec 34° is equal to 1.2062.

What is the Value of Tan 34 Degrees in Terms of Cos 34°?

We know, using trig identities, we can write tan 34° as √(1 - cos²(34°))/cos 34°. Here, the value of cos 34° is equal to 0.829037.

How to Find Tan 34° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 34° can be given in terms of other trigonometric functions as:

• sin(34°)/cos(34°)
• ± sin 34°/√(1 - sin²(34°))
• ± √(1 - cos²(34°))/cos 34°
• ± 1/√(cosec²(34°) - 1)
• ± √(sec²(34°) - 1)
• 1/cot 34°

☛ Also check: trigonometry table

How to Find the Value of Tan 34 Degrees?

The value of tan 34 degrees can be calculated by constructing an angle of 34° with the x-axis, and then finding the coordinates of the corresponding point (0.829, 0.5592) on the unit circle. The value of tan 34° is equal to the y-coordinate(0.5592) divided by the x-coordinate (0.829). ∴ tan 34° = 0.6745