Tan 100 Degrees
The value of tan 100 degrees is -5.6712818. . .. Tan 100 degrees in radians is written as tan (100° × π/180°), i.e., tan (5π/9) or tan (1.745329. . .). In this article, we will discuss the methods to find the value of tan 100 degrees with examples.
- Tan 100° in decimal: -5.6712818. . .
- Tan (-100 degrees): 5.6712818. . .
- Tan 100° in radians: tan (5π/9) or tan (1.7453292 . . .)
What is the Value of Tan 100 Degrees?
The value of tan 100 degrees in decimal is -5.671281819. . .. Tan 100 degrees can also be expressed using the equivalent of the given angle (100 degrees) in radians (1.74532 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 100 degrees = 100° × (π/180°) rad = 5π/9 or 1.7453 . . .
∴ tan 100° = tan(1.7453) = -5.6712818. . .
Explanation:
For tan 100 degrees, the angle 100° lies between 90° and 180° (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 100° value = -5.6712818. . .
Since the tangent function is a periodic function, we can represent tan 100° as, tan 100 degrees = tan(100° + n × 180°), n ∈ Z.
⇒ tan 100° = tan 280° = tan 460°, and so on.
Note: Since, tangent is an odd function, the value of tan(-100°) = -tan(100°).
Methods to Find Value of Tan 100 Degrees
The tangent function is negative in the 2nd quadrant. The value of tan 100° is given as -5.67128. . .. We can find the value of tan 100 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 100° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 100 degrees as:
- sin(100°)/cos(100°)
- ± sin 100°/√(1 - sin²(100°))
- ± √(1 - cos²(100°))/cos 100°
- ± 1/√(cosec²(100°) - 1)
- ± √(sec²(100°) - 1)
- 1/cot 100°
Note: Since 100° lies in the 2nd Quadrant, the final value of tan 100° will be negative.
We can use trigonometric identities to represent tan 100° as,
- cot(90° - 100°) = cot(-10°)
- -cot(90° + 100°) = -cot 190°
- -tan (180° - 100°) = -tan 80°
Tan 100 Degrees Using Unit Circle
To find the value of tan 100 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 100° angle with the positive x-axis.
- The tan of 100 degrees equals the y-coordinate(0.9848) divided by x-coordinate(-0.1736) of the point of intersection (-0.1736, 0.9848) of unit circle and r.
Hence the value of tan 100° = y/x = -5.6713 (approx).
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FAQs on Tan 100 Degrees
What is Tan 100 Degrees?
Tan 100 degrees is the value of tangent trigonometric function for an angle equal to 100 degrees. The value of tan 100° is -5.6713 (approx).
What is the Value of Tan 100° in Terms of Sec 100°?
We can represent the tangent function in terms of the secant function using trig identities, tan 100° can be written as -√(sec²(100°) - 1). Here, the value of sec 100° is equal to -5.7587.
How to Find the Value of Tan 100 Degrees?
The value of tan 100 degrees can be calculated by constructing an angle of 100° with the x-axis, and then finding the coordinates of the corresponding point (-0.1736, 0.9848) on the unit circle. The value of tan 100° is equal to the y-coordinate(0.9848) divided by the x-coordinate (-0.1736). ∴ tan 100° = -5.6713
What is the Value of Tan 100 Degrees in Terms of Cos 100°?
We know, using trig identities, we can write tan 100° as √(1 - cos²(100°))/cos 100°. Here, the value of cos 100° is equal to -0.173648.
How to Find Tan 100° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 100° can be given in terms of other trigonometric functions as:
- sin(100°)/cos(100°)
- ± sin 100°/√(1 - sin²(100°))
- ± √(1 - cos²(100°))/cos 100°
- ± 1/√(cosec²(100°) - 1)
- ± √(sec²(100°) - 1)
- 1/cot 100°
☛ Also check: trigonometric table