Tan 110 Degrees
The value of tan 110 degrees is -2.7474774. . .. Tan 110 degrees in radians is written as tan (110° × π/180°), i.e., tan (11π/18) or tan (1.919862. . .). In this article, we will discuss the methods to find the value of tan 110 degrees with examples.
- Tan 110° in decimal: -2.7474774. . .
- Tan (-110 degrees): 2.7474774. . .
- Tan 110° in radians: tan (11π/18) or tan (1.9198621 . . .)
What is the Value of Tan 110 Degrees?
The value of tan 110 degrees in decimal is -2.747477419. . .. Tan 110 degrees can also be expressed using the equivalent of the given angle (110 degrees) in radians (1.91986 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 110 degrees = 110° × (π/180°) rad = 11π/18 or 1.9198 . . .
∴ tan 110° = tan(1.9198) = -2.7474774. . .
Explanation:
For tan 110 degrees, the angle 110° lies between 90° and 180° (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 110° value = -2.7474774. . .
Since the tangent function is a periodic function, we can represent tan 110° as, tan 110 degrees = tan(110° + n × 180°), n ∈ Z.
⇒ tan 110° = tan 290° = tan 470°, and so on.
Note: Since, tangent is an odd function, the value of tan(-110°) = -tan(110°).
Methods to Find Value of Tan 110 Degrees
The tangent function is negative in the 2nd quadrant. The value of tan 110° is given as -2.74747. . .. We can find the value of tan 110 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 110° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 110 degrees as:
- sin(110°)/cos(110°)
- ± sin 110°/√(1 - sin²(110°))
- ± √(1 - cos²(110°))/cos 110°
- ± 1/√(cosec²(110°) - 1)
- ± √(sec²(110°) - 1)
- 1/cot 110°
Note: Since 110° lies in the 2nd Quadrant, the final value of tan 110° will be negative.
We can use trigonometric identities to represent tan 110° as,
- cot(90° - 110°) = cot(-20°)
- -cot(90° + 110°) = -cot 200°
- -tan (180° - 110°) = -tan 70°
Tan 110 Degrees Using Unit Circle
To find the value of tan 110 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 110° angle with the positive x-axis.
- The tan of 110 degrees equals the y-coordinate(0.9397) divided by x-coordinate(-0.342) of the point of intersection (-0.342, 0.9397) of unit circle and r.
Hence the value of tan 110° = y/x = -2.7475 (approx).
☛ Also Check:
FAQs on Tan 110 Degrees
What is Tan 110 Degrees?
Tan 110 degrees is the value of tangent trigonometric function for an angle equal to 110 degrees. The value of tan 110° is -2.7475 (approx).
How to Find Tan 110° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 110° can be given in terms of other trigonometric functions as:
- sin(110°)/cos(110°)
- ± sin 110°/√(1 - sin²(110°))
- ± √(1 - cos²(110°))/cos 110°
- ± 1/√(cosec²(110°) - 1)
- ± √(sec²(110°) - 1)
- 1/cot 110°
☛ Also check: trigonometric table
What is the Value of Tan 110° in Terms of Sec 110°?
We can represent the tangent function in terms of the secant function using trig identities, tan 110° can be written as -√(sec²(110°) - 1). Here, the value of sec 110° is equal to -2.9238.
What is the Value of Tan 110 Degrees in Terms of Cos 110°?
We know, using trig identities, we can write tan 110° as √(1 - cos²(110°))/cos 110°. Here, the value of cos 110° is equal to -0.342020.
How to Find the Value of Tan 110 Degrees?
The value of tan 110 degrees can be calculated by constructing an angle of 110° with the x-axis, and then finding the coordinates of the corresponding point (-0.342, 0.9397) on the unit circle. The value of tan 110° is equal to the y-coordinate(0.9397) divided by the x-coordinate (-0.342). ∴ tan 110° = -2.7475