Tan 17 Degrees
The value of tan 17 degrees is 0.3057306. . .. Tan 17 degrees in radians is written as tan (17° × π/180°), i.e., tan (0.296705. . .). In this article, we will discuss the methods to find the value of tan 17 degrees with examples.
- Tan 17° in decimal: 0.3057306. . .
- Tan (-17 degrees): -0.3057306. . .
- Tan 17° in radians: tan (0.2967059 . . .)
What is the Value of Tan 17 Degrees?
The value of tan 17 degrees in decimal is 0.305730681. . .. Tan 17 degrees can also be expressed using the equivalent of the given angle (17 degrees) in radians (0.29670 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 17 degrees = 17° × (π/180°) rad = 0.2967 . . .
∴ tan 17° = tan(0.2967) = 0.3057306. . .
Explanation:
For tan 17 degrees, the angle 17° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 17° value = 0.3057306. . .
Since the tangent function is a periodic function, we can represent tan 17° as, tan 17 degrees = tan(17° + n × 180°), n ∈ Z.
⇒ tan 17° = tan 197° = tan 377°, and so on.
Note: Since, tangent is an odd function, the value of tan(-17°) = -tan(17°).
Methods to Find Value of Tan 17 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 17° is given as 0.30573. . .. We can find the value of tan 17 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 17 Degrees Using Unit Circle
To find the value of tan 17 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 17° angle with the positive x-axis.
- The tan of 17 degrees equals the y-coordinate(0.2924) divided by x-coordinate(0.9563) of the point of intersection (0.9563, 0.2924) of unit circle and r.
Hence the value of tan 17° = y/x = 0.3057 (approx).
Tan 17° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 17 degrees as:
- sin(17°)/cos(17°)
- ± sin 17°/√(1 - sin²(17°))
- ± √(1 - cos²(17°))/cos 17°
- ± 1/√(cosec²(17°) - 1)
- ± √(sec²(17°) - 1)
- 1/cot 17°
Note: Since 17° lies in the 1st Quadrant, the final value of tan 17° will be positive.
We can use trigonometric identities to represent tan 17° as,
- cot(90° - 17°) = cot 73°
- -cot(90° + 17°) = -cot 107°
- -tan (180° - 17°) = -tan 163°
☛ Also Check:
FAQs on Tan 17 Degrees
What is Tan 17 Degrees?
Tan 17 degrees is the value of tangent trigonometric function for an angle equal to 17 degrees. The value of tan 17° is 0.3057 (approx).
What is the Value of Tan 17° in Terms of Sec 17°?
We can represent the tangent function in terms of the secant function using trig identities, tan 17° can be written as √(sec²(17°) - 1). Here, the value of sec 17° is equal to 1.0456.
How to Find the Value of Tan 17 Degrees?
The value of tan 17 degrees can be calculated by constructing an angle of 17° with the x-axis, and then finding the coordinates of the corresponding point (0.9563, 0.2924) on the unit circle. The value of tan 17° is equal to the y-coordinate(0.2924) divided by the x-coordinate (0.9563). ∴ tan 17° = 0.3057
How to Find Tan 17° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 17° can be given in terms of other trigonometric functions as:
- sin(17°)/cos(17°)
- ± sin 17°/√(1 - sin²(17°))
- ± √(1 - cos²(17°))/cos 17°
- ± 1/√(cosec²(17°) - 1)
- ± √(sec²(17°) - 1)
- 1/cot 17°
☛ Also check: trigonometry table
What is the Value of Tan 17 Degrees in Terms of Cos 17°?
We know, using trig identities, we can write tan 17° as √(1 - cos²(17°))/cos 17°. Here, the value of cos 17° is equal to 0.956304.