Tan 35 Degrees
The value of tan 35 degrees is 0.7002075. . .. Tan 35 degrees in radians is written as tan (35° × π/180°), i.e., tan (7π/36) or tan (0.610865. . .). In this article, we will discuss the methods to find the value of tan 35 degrees with examples.
- Tan 35° in decimal: 0.7002075. . .
- Tan (-35 degrees): -0.7002075. . .
- Tan 35° in radians: tan (7π/36) or tan (0.6108652 . . .)
What is the Value of Tan 35 Degrees?
The value of tan 35 degrees in decimal is 0.700207538. . .. Tan 35 degrees can also be expressed using the equivalent of the given angle (35 degrees) in radians (0.61086 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 35 degrees = 35° × (π/180°) rad = 7π/36 or 0.6108 . . .
∴ tan 35° = tan(0.6108) = 0.7002075. . .
Explanation:
For tan 35 degrees, the angle 35° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 35° value = 0.7002075. . .
Since the tangent function is a periodic function, we can represent tan 35° as, tan 35 degrees = tan(35° + n × 180°), n ∈ Z.
⇒ tan 35° = tan 215° = tan 395°, and so on.
Note: Since, tangent is an odd function, the value of tan(-35°) = -tan(35°).
Methods to Find Value of Tan 35 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 35° is given as 0.70020. . .. We can find the value of tan 35 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 35° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 35 degrees as:
- sin(35°)/cos(35°)
- ± sin 35°/√(1 - sin²(35°))
- ± √(1 - cos²(35°))/cos 35°
- ± 1/√(cosec²(35°) - 1)
- ± √(sec²(35°) - 1)
- 1/cot 35°
Note: Since 35° lies in the 1st Quadrant, the final value of tan 35° will be positive.
We can use trigonometric identities to represent tan 35° as,
- cot(90° - 35°) = cot 55°
- -cot(90° + 35°) = -cot 125°
- -tan (180° - 35°) = -tan 145°
Tan 35 Degrees Using Unit Circle
To find the value of tan 35 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 35° angle with the positive x-axis.
- The tan of 35 degrees equals the y-coordinate(0.5736) divided by x-coordinate(0.8192) of the point of intersection (0.8192, 0.5736) of unit circle and r.
Hence the value of tan 35° = y/x = 0.7002 (approx).
☛ Also Check:
FAQs on Tan 35 Degrees
What is Tan 35 Degrees?
Tan 35 degrees is the value of tangent trigonometric function for an angle equal to 35 degrees. The value of tan 35° is 0.7002 (approx).
How to Find Tan 35° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 35° can be given in terms of other trigonometric functions as:
- sin(35°)/cos(35°)
- ± sin 35°/√(1 - sin²(35°))
- ± √(1 - cos²(35°))/cos 35°
- ± 1/√(cosec²(35°) - 1)
- ± √(sec²(35°) - 1)
- 1/cot 35°
☛ Also check: trigonometry table
How to Find the Value of Tan 35 Degrees?
The value of tan 35 degrees can be calculated by constructing an angle of 35° with the x-axis, and then finding the coordinates of the corresponding point (0.8192, 0.5736) on the unit circle. The value of tan 35° is equal to the y-coordinate(0.5736) divided by the x-coordinate (0.8192). ∴ tan 35° = 0.7002
What is the Value of Tan 35° in Terms of Sec 35°?
We can represent the tangent function in terms of the secant function using trig identities, tan 35° can be written as √(sec²(35°) - 1). Here, the value of sec 35° is equal to 1.2207.
What is the Value of Tan 35 Degrees in Terms of Cot 35°?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 35° as 1/cot(35°). The value of cot 35° is equal to 1.42814.