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 xaxis.
 The tan of 34 degrees equals the ycoordinate(0.5592) divided by xcoordinate(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:
Examples Using Tan 34 Degrees

Example 1: Find the value of tan 34° if cot 34° is 1.4825.
Solution:
Since, tan 34° = 1/cot 34°
⇒ tan 34° = 1/1.4825 = 0.6745 
Example 2: Simplify: 5 (tan 34°/cot 56°)
Solution:
We know tan 34° = cot 56°
⇒ 5 tan 34°/cot 56° = 5 (tan 34°/tan 34°)
= 5(1) = 5 
Example 3: Find the value of 3 tan(34°)/6 tan(146°).
Solution:
Using trigonometric identities, we know, tan(34°) = tan(180°  34°) = tan 146°.
⇒ tan(34°) = tan(146°)
⇒ Value of 3 tan(34°)/6 tan(146°) = 3/6 = 1/2
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 xaxis, 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 ycoordinate(0.5592) divided by the xcoordinate (0.829). ∴ tan 34° = 0.6745
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